Quasi-orthomodular posets and weak BCK-algebras.
type: Item
instance of: scholarly article
title: Quasi-orthomodular posets and weak BCK-algebras.
zbMATH Open document ID: 1311.06006
author: Jānis Cīrulis
published in: Order
publication date: 2014-10-31T00:00:00Z
review text: A \textit{weak BCK-algebra} (wBCK-algebra for short) is an algebra \((A,-,0)\), where \(A\) is a poset with \(0\) the least element, and \(-\) a total binary operation on \(A\) (called subtraction) satisfying the following axioms: (1) \(x\leq y\) iff \(x-y=0\), and (2) if \(x-y\leq z\), then \(x-z\leq y\). This notion generalizes BCK-algebra. The author is studying orthomodular-type posets (quasi-orthomodular ones, etc.), semilattices, nearlattices and lattices, and compares with each other and with wBCK-algebras.
reviewed by: Anatolij Dvurečenskij
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06F35
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 6363133
zbMATH Keywords: generalized orthoalgebras
zbMATH Keywords: generalized orthomodular lattices
zbMATH Keywords: generalized orthomodular posets
zbMATH Keywords: nearlattices
zbMATH Keywords: quasiorthomodular posets
zbMATH Keywords: relatively orthocomplemented posets
zbMATH Keywords: sectionally orthocomplemented posets
zbMATH Keywords: weak BCK-algebras
MaRDI profile type: Publication
full work available at URL: s11083-013-9309-1
OpenAlex ID: W2063022715
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DOI: 10.1007/S11083-013-9309-1
description: scientific article; zbMATH DE number 6363133