On the mapping xy→(xy)n in an associative ring
نویسندگان
چکیده
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 nonArtinian rings. The results generalize commutativity theorems found elsewhere. The case n(x,y)= 2 is examined in detail.
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004