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  • On Frink Ideals in Orthomodular Posets
    Order Pub Date : 2020-08-03
    Mirko Navara, Pavel Pták

    Let \(\mathcal {S}\) denote the class of orthomodular posets in which all maximal Frink ideals are selective. Let \(\mathcal {R}\) (resp. HCode \(\mathcal {T}\)) be the class of orthomodular posets defined by the validity of the following implications: \(P\in \mathcal {R}\) if the implication a,b ∈ P, \(a\wedge b=0\ \Rightarrow \ a\le b^{\prime }\) holds (resp., \(P\in \mathcal {T}\) if the implication

    更新日期:2020-08-03
  • Relations and Radicals in Abstract Lattices and in Lattices of Subspaces of Banach Spaces and of Ideals of Banach Algebras. Amitsur’s Theory Revisited
    Order Pub Date : 2020-07-29
    Edward Kissin, Victor Shulman, Yuri Turovskii

    We refine Amitsur’s theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattices of ideals of Banach and C*-algebras and of Banach Lie algebras.

    更新日期:2020-07-29
  • Partitioning Transitive Tournaments into Isomorphic Digraphs
    Order Pub Date : 2020-07-23
    Attila Sali, Gábor Simonyi, Gábor Tardos

    In an earlier paper (see Sali and Simonyi Eur. J. Combin. 20, 93–99, 1999) the first two authors have shown that self-complementary graphs can always be oriented in such a way that the union of the oriented version and its isomorphically oriented complement gives a transitive tournament. We investigate the possibilities of generalizing this theorem to decompositions of the complete graph into three

    更新日期:2020-07-23
  • Fully Preorderable Groups
    Order Pub Date : 2020-07-07
    Efe A. Ok, Gil Riella

    We say that a group is fully preorderable if every (left- and right-) translation invariant preorder on it can be extended to a translation invariant total preorder. Such groups arise naturally in applications, and relate closely to orderable and fully orderable groups (which were studied extensively since the seminal works of Philip Hall and A. I. Mal’cev in the 1950s). Our first main result provides

    更新日期:2020-07-07
  • On the Embedding of the Free Lattice of Rank 3 in the Lattice Freely Generated by Three Distributive Type Elements
    Order Pub Date : 2020-06-27
    A. G. Gein, M. P. Shushpanov

    We prove the lattice freely generated by three distributive elements and the lattice freely generated by two distributive elements and one dually distributive element contain the free lattice of rank 3 as sublattice. We describe the lattice freely generated by two distributive elements and one both distributive and dually distributive element. It is infinite, but does not contain the free lattice of

    更新日期:2020-06-27
  • The Frame of Nuclei on an Alexandroff Space
    Order Pub Date : 2020-06-20
    F. Ávila, G. Bezhanishvili, P. J. Morandi, A. Zaldívar

    Let \(\mathcal {O} S\) be the frame of open sets of a topological space S, and let \(N(\mathcal {O} S)\) be the frame of nuclei on \(\mathcal {O} S\). For an Alexandroff space S, we prove that \(N(\mathcal {O} S)\) is spatial iff the infinite binary tree \({\mathscr{T}}_2\) does not embed isomorphically into (S,≤), where ≤ is the specialization preorder of S.

    更新日期:2020-06-22
  • Topos Quantum Theory with Short Posets
    Order Pub Date : 2020-06-19
    John Harding, Chris Heunen

    Topos quantum mechanics, developed by Döring (2008); Döring and Harding Houston J. Math. 42(2), 559–568 (2016); Döring and Isham (2008); Flori 2013)); Flori (2018); Isham and Butterfield J. Theoret. Phys. 37, 2669–2733 (1998); Isham and Butterfield J. Theoret. Phys. 38, 827–859 (1999); Isham et al. J. Theoret. Phys. 39, 1413–1436 (2000); Isham and Butterfield J. Theoret. Phys. 41, 613–639 (2002), creates

    更新日期:2020-06-19
  • Planar Posets that are Accessible from Below Have Dimension at Most 6
    Order Pub Date : 2020-06-02
    Csaba Biró, Bartłomiej Bosek, Heather C. Smith, William T. Trotter, Ruidong Wang, Stephen J. Young

    Planar posets can have arbitrarily large dimension. However, a planar poset of height h has dimension at most 192h + 96, while a planar poset with t minimal elements has dimension at most 2t + 1. In particular, a planar poset with a unique minimal element has dimension at most 3. In this paper, we extend this result by showing that a planar poset has dimension at most 6 if it has a plane diagram in

    更新日期:2020-06-02
  • Linear Extension Numbers of n -Element Posets
    Order Pub Date : 2020-05-11
    Noah Kravitz, Ashwin Sah

    We address the following natural but hitherto unstudied question: what are the possible linear extension numbers of an n-element poset? Let LE(n) denote the set of all positive integers that arise as the number of linear extensions of some n-element poset. We show that LE(n) skews towards the “small” end of the interval [1, n!]. More specifically, LE(n) contains all of the positive integers up to \(\exp

    更新日期:2020-05-11
  • Diagonal Orbits in a Type A Double Flag Variety of Complexity One
    Order Pub Date : 2020-05-06
    Mahir Bilen Can, Tien Le

    We continue our study of the inclusion posets of diagonal SL(n)-orbit closures in a product of two partial flag varieties. We prove that, if the diagonal action is of complexity one, then the poset is isomorphic to one of the 28 posets that we determine explicitly. Furthermore, our computations show that the number of diagonal SL(n)-orbits in any of these posets is at most 10 for any positive integer

    更新日期:2020-05-06
  • Representations of Infinite Tree Sets
    Order Pub Date : 2020-04-28
    J. Pascal Gollin, Jakob Kneip

    Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets. First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order

    更新日期:2020-04-28
  • Containment Graphs and Posets of Paths in a Tree: Wheels and Partial Wheels
    Order Pub Date : 2020-04-27
    Martin Charles Golumbic, Vincent Limouzy

    We consider questions regarding the containment graphs of paths in a tree (CPT graphs), a subclass of comparability graphs, and the containment posets of paths in a tree (CPT orders). In 1984, Corneil and Golumbic observed that a graph G may be CPT, yet not every transitive orientation of G necessarily has a CPT representation, illustrating this on the even wheels W2k(k ≥ 3). Motivated by this example

    更新日期:2020-04-27
  • The Lattice of Functional Alexandroff Topologies
    Order Pub Date : 2020-04-20
    Jacob Menix, Tom Richmond

    If \(f:X \rightarrow X\) is a function, the associated functional Alexandroff topology on X is the topology Pf whose closed sets are \(\{A \subseteq X : f(A) \subseteq A\}\). We present a characterization of functional Alexandroff topologies on a finite set X and show that the collection FA(X) of all functional Alexandroff topologies on a finite set X, ordered by inclusion, is a complemented lattice

    更新日期:2020-04-20
  • Dimension of CPT Posets
    Order Pub Date : 2020-03-26
    Atrayee Majumder, Rogers Mathew, Deepak Rajendraprasad

    A collection of linear orders on X, say \({\mathscr{L}}\), is said to realize a partially ordered set (or poset) \(\mathcal {P} = (X, \preceq )\) if, for any two distinct x,y ∈ X, x ≼ y if and only if x ≺Ly, \(\forall L \in {\mathscr{L}}\). We call \({\mathscr{L}}\) a realizer of \(\mathcal {P}\). The dimension of \(\mathcal {P}\), denoted by \(dim(\mathcal {P})\), is the minimum cardinality of a realizer

    更新日期:2020-03-26
  • On Set-Representable Orthocomplemented Difference Lattices
    Order Pub Date : 2020-03-03
    Jianning Su

    Matoušek introduced and axiomatized a notion of symmetric difference for orthocomplemented lattices (OMLs) called the orthocomplemented difference lattics (ODLs). We focus on the class of all ODLs that are set-representable and prove that this class is not locally finite by constructing an infinite three-generated set-representable ODL. This result answers a question posed by Matoušek and Pták. We

    更新日期:2020-03-03
  • Wonderful Models for Generalized Dowling Arrangements
    Order Pub Date : 2020-02-13
    Giovanni Gaiffi, Viola Siconolfi

    For any triple given by a positive integer n, a finite group G, and a faithful representation V of G, one can describe a subspace arrangement whose intersection lattice is a generalized Dowling lattice in the sense of Hanlon (Trans. Amer. Math. Soc. 325(1), 1–37, 1991). In this paper we construct the minimal De Concini-Procesi wonderful model associated to this subspace arrangement and give a description

    更新日期:2020-02-13
  • Cambrian Acyclic Domains: Counting c -singletons
    Order Pub Date : 2020-02-13
    Jean-Philippe Labbé, Carsten E. M. C. Lange

    We study the size of certain acyclic domains that arise from geometric and combinatorial constructions. These acyclic domains consist of all permutations visited by commuting equivalence classes of maximal reduced decompositions if we consider the symmetric group and, more generally, of all c-singletons of a Cambrian lattice associated to the weak order of a finite Coxeter group. For this reason, we

    更新日期:2020-02-13
  • Generalized Forbidden Subposet Problems
    Order Pub Date : 2020-02-10
    Dániel Gerbner, Balázs Keszegh, Balázs Patkós

    A subfamily \(\{F_{1},F_{2},\dots ,F_{|P|}\}\subseteq \mathcal {F}\) of sets is a copy of a poset P in \(\mathcal {F}\) if there exists a bijection \(\phi :P\rightarrow \{F_{1},F_{2},\dots ,F_{|P|}\}\) such that whenever \(x \le _{P} x^{\prime }\) holds, then so does \(\phi (x)\subseteq \phi (x^{\prime })\). For a family \(\mathcal {F}\) of sets, let \(c(P,\mathcal {F})\) denote the number of copies

    更新日期:2020-02-10
  • On the Largest Numbers of Congruences of Finite Lattices
    Order Pub Date : 2020-01-22
    Claudia Mureşan, Júlia Kulin

    We investigate the possible values of the numbers of congruences of finite lattices of an arbitrary but fixed cardinality. Motivated by a result of Freese and continuing Czédli’s recent work, we prove that the third, fourth and fifth largest numbers of congruences of an n–element lattice are: 5 ⋅ 2n− 5 if n ≥ 5, 2n− 3 and 7 ⋅ 2n− 6 if n ≥ 6, respectively. We also determine the structures of the n–element

    更新日期:2020-01-22
  • Varieties of Regular Pseudocomplemented de Morgan Algebras
    Order Pub Date : 2020-01-10
    M. E. Adams, H. P. Sankappanavar, Júlia Vaz de Carvalho

    In this paper, we investigate the varieties Mn and Kn of regular pseudocomplemented de Morgan and Kleene algebras of range n, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is used. We characterise the dual spaces of the simple (equivalently, subdirectly irreducible) algebras in Mn and explicitly describe the dual spaces of the simple algebras in M1 and K1. We

    更新日期:2020-01-10
  • Weighted Counting of Inversions on Alternating Sign Matrices
    Order Pub Date : 2019-12-27
    Masato Kobayashi

    We generalize the author’s formula (2011) on weighted counting of inversions on permutations to one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix which essentially follows from the earlier work of Lascoux-Schützenberger (1996).

    更新日期:2019-12-27
  • One Hundred Twenty-Seven Subsemilattices and Planarity
    Order Pub Date : 2019-12-18
    Gábor Czédli

    Let L be a finite n-element semilattice. We prove that if L has at least 127 ⋅ 2n− 8 subsemilattices, then L is planar. For n > 8, this result is sharp since there is a non-planar semilattice with exactly 127 ⋅ 2n− 8 − 1 subsemilattices.

    更新日期:2019-12-18
  • Amenable and Locally Amenable Algebraic Frames
    Order Pub Date : 2019-12-13
    Themba Dube

    We say a prime element of an algebraic frame is amenable if it comparable to every compact element. If every prime element of an algebraic frame L is amenable, we say L is an amenable frame. If the localization of L at every prime element is amenable, we say L is locally amenable. These concepts are motivated by notions of divided and locally divided commutative rings. We show that an algebraic frame

    更新日期:2019-12-13
  • Profinite Separation Systems
    Order Pub Date : 2019-12-09
    Reinhard Diestel, Jakob Kneip

    Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory about infinite separation systems and how they relate to the finite separation systems they induce. They can be used to prove tangle-type duality theorems for infinite

    更新日期:2019-12-09
  • A New Characterization of V$\mathcal {V}$ -Posets
    Order Pub Date : 2019-11-22
    Joshua Cooper, Peter Gartland, Hays Whitlatch

    Hasebe and Tsujie characterized the set of induced N-free and bowtie-free posets as a certain class of recursively defined subposets which they term “\(\mathcal {V}\)-posets”. Here we offer a new characterization of \(\mathcal {V}\)-posets by introducing a property we refer to as autonomy. A poset \(\mathcal {P}\) is said to be autonomous if there exists a directed acyclic graph D (with adjacency matrix

    更新日期:2019-11-22
  • Separations of Sets
    Order Pub Date : 2019-11-19
    Nathan Bowler, Jakob Kneip

    Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as separation systems of graphs, sets, or set bipartitions.

    更新日期:2019-11-19
  • Universality Property and Dimension for Frames
    Order Pub Date : 2019-11-19
    D. Georgiou, S. Iliadis, A. Megaritis, F. Sereti

    The universality property plays an important role in the field of frames and the notion of saturated class of frames is combined with this property (see Dube et al. (Topology and its Applications 160, 2454–2464, 2013); Iliadis (Topology and its Applications 179, 99–110, 2015) and Iliadis (Topology and its Applications 201, 92–109, 18)). In this paper, we continue such a study, introducing and studying

    更新日期:2019-11-19
  • On Monomial Ideals and Their Socles
    Order Pub Date : 2019-11-16
    Geir Agnarsson, Neil Epstein

    For a finite subset M ⊂ [x1,…, xd] of monomials, we describe how to constructively obtain a monomial ideal \(I\subseteq R = K[x_{1},\ldots ,x_{d}]\) such that the set of monomials in Soc(I) ∖ I is precisely M, or such that \(\overline {M}\subseteq R/I\) is a K-basis for the the socle of R/I. For a given M we obtain a natural class of monomials ideals I with this property. This is done by using solely

    更新日期:2019-11-16
  • Ambiguous Representations of Semilattices, Imperfect Information, and Predicate Transformers
    Order Pub Date : 2019-11-07
    Oleh Nykyforchyn, Oksana Mykytsey

    Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, for which taking pseudo-inverse is involutive, form categories. Self-dualities and contravariant equivalences for these categories are obtained

    更新日期:2019-11-07
  • Investigating posets via their maximal chains
    Order Pub Date : 2019-10-22
    Seyed Hadi Afzali Borujeni, Nathan Bowler

    By considering the number of maximal chains going through each element of an arbitrary poset, we prove an extension of Erdős’s generalisation of Sperner’s Theorem, together with a partial converse. By considering the number of maximal chains between pairs of comparable elements, we also prove a generalisation of the LYM inequality.

    更新日期:2019-10-22
  • Path Counting and Rank Gaps in Differential Posets
    Order Pub Date : 2019-09-21
    Christian Gaetz, Praveen Venkataramana

    We study the gaps Δpn between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δpn ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δpn ≥ 2r. We also obtain stronger bounds in the case that the poset has many

    更新日期:2019-09-21
  • Boolean Dimension, Components and Blocks
    Order Pub Date : 2019-09-14
    Tamás Mészáros, Piotr Micek, William T. Trotter

    We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for Dushnik-Miller dimension, we have that if \(\dim (C)\le d\) for every component C of a poset P, then \(\dim (P)\le \max \limits \{2,d\}\); also if \(\dim (B)\le d\) for every block B of a poset P, then \(\dim (P)\le d+2\). By way of constrast, local dimension is well

    更新日期:2019-09-14
  • A Note on the Modularization of Lattices
    Order Pub Date : 2019-09-04
    Yibo Gao

    Valuations on finite lattices have been known for a long time. In this paper, we present a combinatorial procedure called modularization that associates a modular lattice to any given finite lattice such that they have the same valuation polytopes.

    更新日期:2019-09-04
  • Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
    Order Pub Date : 2019-08-16
    Fidel Barrera-Cruz, Thomas Prag, Heather C. Smith, Libby Taylor, William T. Trotter

    The original notion of dimension for posets is due to Dushnik and Miller and has been studied extensively in the literature. Quite recently, there has been considerable interest in two variations of dimension known as Boolean dimension and local dimension. For a poset P, the Boolean dimension of P and the local dimension of P are both bounded from above by the dimension of P and can be considerably

    更新日期:2019-08-16
  • The Lattice of Varieties of Implication Semigroups
    Order Pub Date : 2019-08-03
    Sergey V. Gusev, Hanamantagouda P. Sankappanavar, Boris M. Vernikov

    An implication semigroup is an algebra of type (2, 0) with a binary operation → and a 0-ary operation 0 satisfying the identities \((x\rightarrow y)\rightarrow z\approx x\rightarrow (y\rightarrow z)\), \((x\rightarrow y)\rightarrow z\approx \left [(z^{\prime }\rightarrow x)\rightarrow (y\rightarrow z)'\right ]'\) and \(0^{\prime \prime }\approx 0\) where \(\mathbf {u}^{\prime }\) means \(\mathbf u\rightarrow

    更新日期:2019-08-03
  • Avoiding Brooms, Forks, and Butterflies in the Linear Lattices
    Order Pub Date : 2019-07-24
    Shahriar Shahriari, Song Yu

    Let n be a positive integer, q a power of a prime, and \(\mathcal {L}_{n}({q})\) the poset of subspaces of an n-dimensional vector space over a field with q elements. This poset is a normalized matching poset and the set of subspaces of dimension ⌊n/2⌋ or those of dimension ⌈n/2⌉ are the only maximum-sized antichains in this poset. Strengthening this well-known and celebrated result, we show that,

    更新日期:2019-07-24
  • On Lattice Representations with Dcc Posets
    Order Pub Date : 2019-07-20
    Gergő Gyenizse

    In this paper, we investigate the class of lattices representable with posets satisfying the DCC condition. We describe a way to decide whether a finite lattice is in this class. We also give a necessary condition for an arbitrary lattice to be in this class. This hints at a notion that would be a weaker version of lower boundedness.

    更新日期:2019-07-20
  • Posets of Copies of Countable Non-Scattered Labeled Linear Orders
    Order Pub Date : 2019-06-26
    Miloš S. Kurilić, Stevo Todorčević

    We show that the poset of copies \(\mathbb {P} (\mathbb {Q}_{n} )=\langle \{ f[X]: f\in \text {Emb} (\mathbb {Q}_{n} ) \},\subset \rangle \) of the countable homogeneous universal n-labeled linear order, \(\mathbb {Q}_{n}\), is forcing equivalent to the poset \(\mathbb {S} \ast \pi \), where \(\mathbb {S}\) is the Sacks perfect set forcing and \(1_{\mathbb {S}} \Vdash `` \pi \) is an atomless separative

    更新日期:2019-06-26
  • Classes of (0,1)-matrices Where the Bruhat Order and the Secondary Bruhat Order Coincide
    Order Pub Date : 2019-06-19
    Rosário Fernandes, Henrique F. da Cruz, Domingos Salomão

    Given two nonincreasing integral vectors R and S, with the same sum, we denote by \(\mathcal {A}(R,S)\) the class of all (0,1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on \(\mathcal {A}(R,S)\) are both extensions of the classical Bruhat order on Sn, the symmetric group of degree n. These two partial orders on \(\mathcal {A}(R,S)\) are

    更新日期:2019-06-19
  • Fixed Point Property for Finite Ordered Sets that Contain No Crowns with 6 or More Elements
    Order Pub Date : 2019-06-10
    Bernd S. W. Schröder

    We prove that, for a finite ordered set P that contains no crowns with 6 or more elements, it can be determined in polynomial time if P has the fixed point property. This result is obtained by proving that every such ordered set must contain a point of rank 1 that has a unique lower cover or a retractable minimal element.

    更新日期:2019-06-10
  • A Discrete Duality Between Nonmonotonic Consequence Relations and Convex Geometries
    Order Pub Date : 2019-06-10
    Johannes Marti, Riccardo Pinosio

    In this paper we present a duality between nonmonotonic consequence relations and well-founded convex geometries. On one side of the duality we consider nonmonotonic consequence relations satisfying the axioms of an infinitary variant of System P, which is one of the most studied axiomatic systems for nonmonotonic reasoning, conditional logic and belief revision. On the other side of the duality we

    更新日期:2019-06-10
  • Connectivity Properties of Factorization Posets in Generated Groups
    Order Pub Date : 2019-06-10
    Henri Mühle, Vivien Ripoll

    We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework

    更新日期:2019-06-10
  • Reversible Disjoint Unions of Well Orders and Their Inverses
    Order Pub Date : 2019-06-07
    Miloš S. Kurilić, Nenad Morača

    A poset \(\mathbb {P}\) is called reversible iff every bijective homomorphism \(f:\mathbb {P} \rightarrow \mathbb {P}\) is an automorphism. Let \(\mathcal {W}\) and \(\mathcal {W}^{*}\) denote the classes of well orders and their inverses respectively. We characterize reversibility in the class of posets of the form \(\mathbb {P} =\bigcup _{i\in I}\mathbb {L}_{i}\), where \(\mathbb {L}_{i}, i\in I\)

    更新日期:2019-06-07
  • Z$\mathcal {Z}$ -quasidistributive and Z$\mathcal {Z}$ -meet-distributive Posets
    Order Pub Date : 2019-05-25
    Wenfeng Zhang, Xiaoquan Xu

    Given any subset selection \(\mathcal {Z}\) for posets, we study two weakenings of the known concept of \(\mathcal {Z}\)-predistributivity, namely, \(\mathcal {Z}\)-quasidistributivity and \(\mathcal {Z}\)-meet-distributivity. The former generalizes quasicontinuity, and the latter meet-continuity of complete lattices. We show for global completions \(\mathcal {Z}\) that the \(\mathcal {Z}\)-quasidistributive

    更新日期:2019-05-25
  • Efficient Removal Lemmas for Matrices
    Order Pub Date : 2019-05-23
    Noga Alon, Omri Ben-Eliezer

    It was recently proved in Alon et al. (2017) that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a constant number of queries, by establishing the following ordered matrix removal lemma: For any finite alphabet Γ, any hereditary property \(\mathcal {P}\) of matrices over Γ, and any 𝜖 > 0, there exists \(f_{\mathcal

    更新日期:2019-05-23
  • Associative, Idempotent, Symmetric, and Order-preserving Operations on Chains
    Order Pub Date : 2019-05-04
    Jimmy Devillet, Bruno Teheux

    We characterize the associative, idempotent, symmetric, and order-preserving binary operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilattice order. In particular, we prove that the number of associative, idempotent, symmetric, and order-preserving operations on an n-element chain is the nth Catalan number.

    更新日期:2019-05-04
  • Algebraic Aspects of Relatively Pseudocomplemented Posets
    Order Pub Date : 2019-05-01
    Ivan Chajda, Helmut Länger, Jan Paseka

    In Chajda and Länger (Math. Bohem. 143, 89–97, 2018) the concept of relative pseudocomplementation was extended to posets. We introduce the concept of a congruence in a relatively pseudocomplemented poset within the framework of Hilbert algebras and we study under which conditions the quotient structure is a relatively pseudocomplemented poset again. This problem is solved e.g. for finite or linearly

    更新日期:2019-05-01
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