On the mapping xy→(xy)n in an associative ring
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 rin...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204208250 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |