Herstein猜测

ON Herstein CONJECTURE

证明了在几种特殊情形下的Ｈｅｒｓｔｅｉｎ猜测的正确性。假设Ｒ是一个左Ｎｏｅｔｈｅｒ环，且有左理想ＩＪ，使得Ｊ在Ｉ上为诣零的，那么Ｊ在Ｉ上为幂零的，在如下情形时：（ａ）当Ｊ／Ｉ是左ＡｒｔｉｎＲ－模；（ｂ）当Ｒ是左完全有界环；（ｃ）当Ｒ是单环；（ｄ）当Ｒ＝ＺＧ是有限群Ｇ的多循环的整群环。

This paper proves that Herstein's conjecture is true in a number of special cases.Let R be a left Noetherian ring with left ideals IJ such that J is nil over I.The J is nilpotent over I in the following cases: \ \ (a)\ When J/I is a left Artinian R-module; \ \ (b)\ When R is a left fully bounded ring; \ \ (c)\ When R is simple ring; \ \ (d)\ When R=ZG is the integral group ring of a poly-cyclic by finite group G.