Congruences, ideals and annihilators in standard QBCC-algebras
type: Item
instance of: scholarly article
title: Congruences, ideals and annihilators in standard QBCC-algebras
zbMATH Open document ID: 1071.06011
DOI: 10.2478/BF02475657
author: Radomír Halaš
author: Luboš Plojhar
published in: Central European Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: An algebra \((A,\circ, 1)\) of type \((2,0)\) is called a QBCC-algebra if it satisfies the following axioms: (1) \((x\circ y)\circ[(z\circ x)\circ(z \circ y)]= 1\), (2) \(x\circ x= 1\), (3) \(x\circ 1= x\), (4) \(1\circ x= x\). A QBCC-algebra is called standard if every subset containing 1 is a subalgebra. For \(a\in A\), a subset \(C(a)= \{x\in A\mid a\leq x\) and \(x\leq a\}\) is called the cell of \(a\), where \(x\leq y\) is defined by \(x\circ y= 1\). The authors show the following characterization theorem for the congruence lattices \(\text{Con}(A)\) of the standard QBCC-algebra \(A\) to be distributive: Theorem 2.2. \(\text{Con}(A)\) is distributive if and only if \(A\) contains at most two-element cells.
reviewed by: Michiro Kondo
Mathematics Subject Classification ID: 06F35
zbMATH DE Number: 2143660
zbMATH Keywords: congruence
zbMATH Keywords: ideal
zbMATH Keywords: annihilator
zbMATH Keywords: BCC-algebra
zbMATH Keywords: QBCC-algebra
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2478/bf02475657
OpenAlex ID: W2086901755
description: scientific article; zbMATH DE number 2143660