环的几个交换性定理

Some Commutativity Theorems on Rings

本文证明了环的几个交换性定理,推广了Asharf的结果。

The present paper covers several commutativity theorems for rings. The results obtained by Asharf in [1] are extended. The main result is the following theorem:Theorem Let R be a ring , if for any y∈R, there exist m=m(y), n=n(y), s=s(y)≥0 and f_y(t)∈{t^2g(t)|g(t)∈Z[t]), [x,x^3y-x^mf(y)x^n]=0 for any x∈R. Then(1) R is Commutative if R is a semi-prime ring;(2) R is commutative if R is a left S-unital ring.