Equational definability of addition in certain noncommutative rings
type: Item
instance of: scholarly article
title: Equational definability of addition in certain noncommutative rings
zbMATH Open document ID: 0548.16034
DOI: 10.1016/0021-8693(85)90141-3
author: Adil Yaqub
author: Mohan S. Putcha
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: It is shown that if R is a ring with unity 1, not necessarily commutative which satisfies the identity \(x^ n=x^{n+1}f(x)\), where n is a fixed positive integer and f(x) is a fixed polynomial with integer coefficients, then the addition \(''+''\) of R is equationally definable in terms of multiplication ''\(\times ''\) and the successor operation ''{\^{\ }}'' (x{\^{\ }}\(=x+1)\).
Mathematics Subject Classification ID: 16Y99
Mathematics Subject Classification ID: 06E20
Mathematics Subject Classification ID: 16Rxx
zbMATH DE Number: 3873553
zbMATH Keywords: addition
zbMATH Keywords: equationally definable
reviewed by: Manuel Abad
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90141-3
OpenAlex ID: W1993802412
cites work: Q3876073
cites work: Equational definability of addition in certain rings
cites work: The Theory of Representation for Boolean Algebras
cites work: On the Theory of Ring-Logics
cites work: On certain finite rings and ring-logics
cites work: Ring-logics and residue class rings
Recommended article: On equational theories of classes of nonassociative rings
Recommended article: On additive maps and commutativity in rings
Recommended article: Equational elements in additive algebras
Recommended article: Commutativity of rings involving additive mappings
Recommended article: On the addition of units and non-units in finite commutative rings
Recommended article: On definability of addition in Lie algebras
Recommended article: Q3197966
Recommended article: Certain additive decompositions in a noncommutative ring
Recommended article: Q3708939
description: scientific article; zbMATH DE number 3873553