On a commutativity conditions of semi-prime rings;

Gave some commutatirity conditions of semi-prime ring, which is a generalization of related results in [2,4-11

Gave some commutativity theorems of semi-prime ring,which is a generalization of relatedin.

Some commutative conditions of semiprime rings with two substructures

This paper proved a commutativity theorem on semiprime rings as follows:for any a,c∈R,b∈Z(R)\｛0｝,there must exist a polynomial f(x,y) with integer coefficient depending on a,b and c,such that [a-f(a,b),c]∈Z(R)then R is commutative.

In this paper,we give a commutativity result for semiprime rings,which generalizes some related results in references[3]～[21].

Two commutativity theorem of semi-prime rings;

Study on central commutator conditions on semi-prime rings;

In this paper, the author proved the following commutativity theorem on semi-prime rings: Let R be semi -prime rings, for any x, y∈R, there exist integers s=s(x)>1, t=t(x)>1 (or s=s(y)>1, t=t(y)>1), such that [xy, xxyt]∈Z(R), then R is commutative.

There are two commutativity theorems on ring as follows: 1)Let R be semiprime ring for any x,y∈R,there exist integers m=m(y)≥0,n=n(y)≥0,m≥n,fx,y(t)∈t2Z[t],such that fx,y(xmy)-yxn∈Z(R) or fx,y(yxm)-yxn∈Z(R),then R is commutative.

Some centre elemene and commutativity theorems of semiprime rings are given, some results in paper [2, 3] are extened.

We get some new results on commutativity of rings by studying the K?the semisimple ring, semiprime ring and arbitrary ring.