Pseudo-BCH Semilattices

Andrzej Walendziak

doi:10.18778/0138-0680.47.2.04

Authors

Andrzej Walendziak Faculty of Sciences, Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, ul. 3 Maja 54, 08-110 Siedlce, Poland

DOI:

https://doi.org/10.18778/0138-0680.47.2.04

Keywords:

(pseudo-)BCK/BCI/BCH algebra, pseudo-BCH join (meet)-semilattice, weakly regular, arithmetical at 1

Abstract

In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.

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