Some commutativity results for associative rings with unit

The commutative theory of associative ring is the main contents of ring theory, it is a fundamental of commutative algebra and algebra number theory. the structural problem of rings with unit has been a main content for ring theory, in particular, for commutativity problem of polynomial identity rings. In this paper, the structural problem of PI-rings has been investigated, improved from fixed value or only positive integer variate y to that the degree of polynomial have correlation with not only variate of polynomial y but also variate of polynomial x , some novel commutative results have been obtained.