满足(xy)~n=x^sy^t条件的环的交换性

Commutativity of Rings Satisfying (xy)~n=x^sy^t

证明了当R是Kothe半单纯环，若，均有依与它们的自然数n(x,y)＞1和s(x,y)与t(x，y)（2n≠s＋t），使得（xy)n=xsyt，则R是交换环的结论．

In this paper, the conunutativity of a ring satisfying (xy)n=fsyt is studied and thefollowing result is proved: Suppose that R is a Kothe selin-simple ring, if there arepositive integers n(x, y)>1 and t(x, y) satisfying 2n≠s+t and (xy)n=xsyt, then R is commtative.