On the mapping x y → ( x y ) n in an associative ring

Scott J. Beslin and Awad Iskander

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-4

Abstract:

We consider the following condition (*) on an associative ring R : ( * ) . There exists a function f from R into R such that f is a group homomorphism of ( R , + ) , f is injective on R 2 , and f ( x y ) = ( x y ) n ( x , y ) for some positive integer n ( x , y ) > 1 . Commutativity and structure are established for Artinian rings R satisfying (*), and a counterexample is given for non-Artinian rings. The results generalize commutativity theorems found elsewhere. The case n ( x , y ) = 2 is examined in detail.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:106524

DOI: 10.1155/S0161171204208250

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