Powers of Commutators and Anticommutators. (24th December 2012)

• Record Type: Journal Article
• Authors: Buckley, Stephen M.; MacHale, Desmond
• Other Names: Anderson D. Academic Editor.; Kelarev A. V. Academic Editor.; Kiliçman A. Academic Editor.; Sage D. Academic Editor.; Zimmermann A. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2012(2012)
• Publication Date: 2012-12-24
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2012/302524
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : For n = 3, 4, we give elementary proofs of commutativity of rings in which the identity c n = c holds for all commutators c . For even n, we show that the commutativity of rings satisfying such an identity is equivalent to the anticommutativity of rings satisfying the corresponding anticommutator equation.