Ideals and congruences of basic algebras
type: Item
instance of: scholarly article
title: Ideals and congruences of basic algebras
zbMATH Open document ID: 1271.03087
author: Ivan Chajda
author: Jan Kühr
published in: Soft Computing
publication date: 2013-06-11T00:00:00Z
review text: According to [\textit{I. Chajda} et al., Algebra Univers. 60, No. 1, 63--90 (2009; Zbl 1219.06013)], a \textit{basic algebra} is an algebra \((A;\oplus,\neg,0, 1)\) such that {\parindent=6mm \begin{itemize}\item[1.] \(x\oplus 0=x,\) \item[2.] \(\neg \neg x = x,\) \item[3.] \(\neg(\neg x \oplus y)\oplus y = \neg (\neg y \oplus x) \oplus x,\) \item[4.] \(\neg(\neg(\neg(x\oplus y)\oplus y)\oplus z)\oplus (x \oplus z)=1.\) \end{itemize}} Examples of basic algebras are MV-algebras and effect algebras. The main aim of the paper under review is to present an internal characterization of congruence kernels that are ideals of basic algebras, and to find a finite basis of ideal terms. In addition, these bases are used to axiomatize the subvariety generated by linearly ordered basic algebras.
reviewed by: Anatolij Dvurečenskij
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 6173756
zbMATH Keywords: basic algebra
zbMATH Keywords: congruence
zbMATH Keywords: ideal
zbMATH Keywords: ideal term
zbMATH Keywords: effect algebra
MaRDI profile type: Publication
full work available at URL: s00500-012-0915-4
OpenAlex ID: W2080236494
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DOI: 10.1007/S00500-012-0915-4
description: scientific article; zbMATH DE number 6173756