on the mapping xy→(xy)n in an associative ring
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ID: 174485
2004
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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 R2, and f(xy)=(xy)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.
| Reference Key |
beslin2004internationalon
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|---|---|
| Authors | ;Scott J. Beslin;Awad Iskander |
| Journal | structural engineering and mechanics |
| Year | 2004 |
| DOI |
10.1155/S0161171204208250
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| URL | |
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