Regularity in terms of hyperideals.
type: Item
instance of: scholarly article
title: Regularity in terms of hyperideals.
zbMATH Open document ID: 1311.20069
DOI: 10.1155/2013/167037
author: Kostaq Hila
author: Bijan Davvaz
author: Krisanthi Naka
author: Jani Dine
published in: Chinese Journal of Mathematics
publication date: 2014-10-16T00:00:00Z
reviewed by: Ali Madanshekaf
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 08A02
zbMATH DE Number: 6356616
zbMATH Keywords: \(n\)-ary hyperoperations
zbMATH Keywords: regularity
zbMATH Keywords: hyperideals
Wikidata QID: Q58920736
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/167037
OpenAlex ID: W2077017809
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cites work: On special classes of n-algebras
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cites work: A Generalization ofn-Ary Algebraic Systems
cites work: NEUTRAL ELEMENTS, FUNDAMENTAL RELATIONS AND n-ARY HYPERSEMIGROUPS
cites work: A characterisation of regular semi-group
cites work: Q3232335
cites work: A remark on regular semigroups
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review text: The paper deals with the notion of regularity in algebraic hypersystems. By an algebraic hypersystem \((H,f_1,\ldots,f_n)\) is meant a non-empty set \(H\) closed under a collection of \(m_i\)-ary \textit{hyperoperations} \(f_i\), i.e., \(f_i\colon\underbrace{H\times\cdots\times H}_{m_i\text{-times}}\to\mathcal P^*(H)\) is a mapping for \(1\leq i\leq n\), and often also satisfying a fixed set of laws, for instance, the associative law.NEWLINENEWLINE In classical semigroup theory it is well known that the notion of regularity can be stated in terms of ideals. For example, a commutative semigroup is regular if and only if every ideal is idempotent. In this paper the authors first define the notion of regularity in an algebraic hypersystem \((H,f)\) and then prove similar result for this hypersystem. (Note: The correct publication year of ref. [12] in the paper is 1956.)
description: scientific article; zbMATH DE number 6356616