The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular lattice N₅. The aim of this paper is to extend the concept of sectional pseudocomplementation from lattices to posets. At first we show that the class of sectionally pseudocomplemented lattices forms a variety of lattices which can be described by two simple identities. This variety has nice congruence properties. We summarize properties of sectionally pseudocomplemented posets and show differences to relative pseudocomplementation. We prove that every sectionally pseudocomplemented poset is completely L-semidistributive. We introduce the concept of congruence on these posets and show when the quotient structure becomes a poset again. Finally, we study the Dedekind-MacNeille completion of sectionally pseudocomplemented posets. We show that contrary to the case of relatively pseudocomplemented posets, this completion need not be sectionally pseudocomplemented but we present the construction of a so-called generalized ordinal sum which enables us to construct the Dedekind-MacNeille completion provided the completions of the summands are known.

Birkhoff（1979）引入了分段伪互补格的概念，作为对不一定是分布晶格的相对伪互补的扩展。这种晶格的典型例子是非模块化晶格N ₅。本文的目的是将分段伪互补的概念从晶格扩展到波峰。首先，我们证明了截面伪互补格的类别形成了可以用两个简单的恒等式描述的各种格。这个品种具有很好的一致性特性。我们总结了部分伪补足的性质，并显示了相对伪补足的差异。我们证明每个分段伪互补的摆姿完全是L-半分配。我们在这些球状体上引入全等概念，并显示商结构何时再次变为一个球状体。最后，我们研究了部分伪互补型球的Dedekind-MacNeille完成。我们表明，与相对伪补足的情况相反，该完成不需要分段伪补，但是我们提出了所谓的广义序数和的构造，如果已知被加数的补全，则该构造使我们能够构造Dedekind-MacNeille补全。 。