Open AccessOn commutativity of rings with conditions involving elements and the Jacobson radical
Author(s) -
Murtaza A. Quadri,
Mohd Shadab Khan
Publication year - 2002
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2002.06.01
Subject(s) - jacobson radical , commutative property , mathematics , associative property , torsion (gastropod) , commutative ring , integer (computer science) , pure mathematics , ring (chemistry) , combinatorics , discrete mathematics , chemistry , computer science , anatomy , medicine , organic chemistry , programming language
Let R be an associative ring with unity 1, N the set of nilpotents, J the Jacobson radical of R and n>1 be a fixed integer. We prove that if R is n(n+1)-torsion free and satisfies the identity (xy)n=ynxn for all x,y ∈ R\ (N ∪ J), then R is commutative.