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Varieties of semiassociative relation algebras and tense algebras
Algebra universalis ( IF 0.6 ) Pub Date : 2020-03-31 , DOI: 10.1007/s00012-020-0646-9
James M. Koussas , Tomasz Kowalski

It is well known that the subvariety lattice of the variety of relation algebras has exactly three atoms. The (join-irreducible) covers of two of these atoms are known, but a complete classification of the (join-irreducible) covers of the remaining atom has not yet been found. These statements are also true of a related subvariety lattice, namely the subvariety lattice of the variety of semiassociative relation algebras. The present article shows that this atom has continuum many covers in this subvariety lattice (and in some related subvariety lattices) using a previously established term equivalence between a variety of tense algebras and a variety of semiassociative \(r\)-algebras.



中文翻译:

半缔合关系代数和时态代数的变体

众所周知,各种关系代数的子变量格恰好具有三个原子。这些原子中的两个的(不可还原的)盖是已知的,但尚未找到剩余原子的(不可还原的)盖的完整分类。这些陈述也适用于相关的子变量格,即各种半缔合关系代数的子变量格。本文表明,该原子使用先前确定的各种时态代数和各种半缔合\(r \)-代数之间的等价项,在该子变种格(以及一些相关的子变种格)中具有连续的许多覆盖。

更新日期:2020-03-31
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