1, Gave some commutativity theorems of semi - prime ring, which is a generalization of related in.

2, Some centre element and commutativity theorems of semiprime rings are given, some results in are extened.

3, The present paper presents a commutativity theorem of rings with identity.

4, It is possible to use kronecker products to overcome some of the snags arising from non - commutativity.

5, Further on, we can specify an algebra that consists of axioms for commutativity, distributivity, associativity, etc.

6, We study in this paper the structure of additive mappings on triangular matrix algebras which preserve commutativity.

7, We won't run into any problem of non - commutativity in constructing these operators.

8, There is no convergence trouble here, but there may be commutativity trouble.