\((3,3)\)-ary differential rings.
type: Item
instance of: scholarly article
title: \((3,3)\)-ary differential rings.
zbMATH Open document ID: 1269.16044
author: Lily Zareyan
author: Bijan Davvaz
author: V. Leoreanu-Fotea
published in: Mediterranean Journal of Mathematics
publication date: 2012-11-15T00:00:00Z
review text: A \((3,3)\)-ary differential ring is a system \((R,f,g,\Delta)\) where \(R\) is a nonempty set, \(f\) and \(g\) are ternary compositions such that \((R,f)\) is a ternary Abelian group with a neutral element, \(g\) is associative and tridistributive with respect to \(f\), \(\Delta\) is a set of derivations such that for each derivation \(d\) and every \(x,y,z\) in \(R\), \(d(f(x,y,z))=f(d(x),d(y),d(z))\) and \(d(g(x,y,z))=f(g(d(x),y,z),g(x,d(y),z),g(x,y,d(z))\). The authors introduce and study some concepts as ideals of \(R\), semiprime and prime ideals, radicals, nilradical. In the last section, applications to hypergroups and ternary hypergroups with orderings, and to automata are given.
reviewed by: Mirela Ştefănescu
Mathematics Subject Classification ID: 16Y99
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 20N10
Mathematics Subject Classification ID: 20N15
Mathematics Subject Classification ID: 20N20
zbMATH DE Number: 6107815
zbMATH Keywords: differential rings
zbMATH Keywords: derivations
zbMATH Keywords: semihypergroups
zbMATH Keywords: ternary hypergroups
zbMATH Keywords: ternary Abelian groups
MaRDI profile type: Publication
full work available at URL: s00009-011-0124-x
OpenAlex ID: W1979478173
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DOI: 10.1007/S00009-011-0124-X
description: scientific article; zbMATH DE number 6107815