On idempotent and hyperassociative structures
type: Item
instance of: scholarly article
title: On idempotent and hyperassociative structures
zbMATH Open document ID: 1439.08002
DOI: 10.1134/S1995080219080171
author: Marlen Yolchyan
author: Yuri Movsisyan
published in: Lobachevskii Journal of Mathematics
publication date: 2019-12-03T00:00:00Z
review text: An algebra with binary operations is called a binary algebra. A binary algebra \((Q;\Sigma)\) is said to be 1) hyperassociative if \(X(x,Y(y,z))=Y(X(x,y),z)\) for every operations \(X,Y\in\Sigma\), 2) rectangular if \(X(x,X(y,x))=x\) for every operation \(X\in\Sigma\). The main result of the paper under review is Theorem 4. Let \((Q;\Sigma)\) be an idempotent and hyperassociative binary algebra. Then if there exists on it such a congruence that corresponding quotient algebra is a rectangular semigroup and operations of the set are semilattice operations on each equivalence class then \((Q;\Sigma)\) satisfies the transitive commutativity property \(X(x,y)=X(y,x)\) and \(X(y,z)=X(z,y)\Rightarrow X(x,z)=X(z,x)\).
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 7139458
zbMATH Keywords: hyperidentity
zbMATH Keywords: binary algebra
zbMATH Keywords: congruence
zbMATH Keywords: rectangular algebra
zbMATH Keywords: semilattice
zbMATH Keywords: idempotent and hyperassociative algebra
zbMATH Keywords: transitive commutativity property
reviewed by: V. N. Saliĭ
MaRDI profile type: Publication
cites work: Q3934450
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cites work: Idempotent semigroups with transitive commutativity relation.
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full work available at URL: s1995080219080171
OpenAlex ID: W2972150407
Wikidata QID: Q127322483
description: scientific article; zbMATH DE number 7139458