\(\nu\)-regular Menger algebras
type: Item
instance of: scholarly article
title: \(\nu\)-regular Menger algebras
zbMATH Open document ID: 0906.20048
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: A Menger algebra of rank \(n\) is an algebra of the form \((G,\cdot)\), where \(\cdot\colon(x,y_1,\ldots,y_n)\to x[y_1\ldots y_n]\) is an \((n+1)\)-ary operation on \(G\) satisfying the superassociativity law \(x[y_1\ldots y_n][z_1\ldots z_n]=x[y_1[z_1\ldots z_n]\ldots y_n[z_1\ldots z_n]]\), where \(x[y_1\ldots y_n][z_1\ldots z_n]=(x[y_1\ldots y_n])[z_1\ldots z_n]\). They are a natural generalization of semigroups. \((G,\cdot)\) is called \(\nu\)-regular if for every vector \((g_1,\ldots,g_n)\in G^n\) there exists some \(x\in G\) such that the equalities \(g_i[x\ldots x][g_1\ldots g_n]=g_i\) are true for each \(i=1,\ldots,n\). In the present paper some properties of \(\nu\)-regular Menger algebras concerning idempotents and inverse elements similar to properties known for semigroups are proved.
Mathematics Subject Classification ID: 20N15
Mathematics Subject Classification ID: 20M99
zbMATH DE Number: 1226232
zbMATH Keywords: Menger algebras
zbMATH Keywords: superassociativity
zbMATH Keywords: idempotents
zbMATH Keywords: inverses
zbMATH Keywords: \(n\)-ary operations
zbMATH Keywords: identities
author: Valentin S. Trokhimenko
reviewed by: Radomír Halaš
MaRDI profile type: Publication
full work available at URL: s000120050044
OpenAlex ID: W2023715053
DOI: 10.1007/S000120050044
description: scientific article; zbMATH DE number 1226232