Open AccessPowers of Commutators and Anticommutators
Author(s) -
Stephen M. Buckley,
Desmond MacHale
Publication year - 2012
Publication title -
isrn algebra
Language(s) - English
Resource type - Journals
eISSN - 2090-6293
pISSN - 2090-6285
DOI - 10.5402/2012/302524
Subject(s) - mathematical proof , commutative property , identity (music) , mathematics , pure mathematics , jacobi identity , algebra over a field , physics , geometry , lie algebra , acoustics
For , we give elementary proofs of commutativity of rings in which the identity holds for all commutators . For even , we show that the commutativity of rings satisfying such an identity is equivalent to the anticommutativity of rings satisfying the corresponding anticommutator equation.
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