广义周期环

给出了广义周期环的一些刻划，证明了半质的广义周期环或是交换环或是诣零环和P2-环的直和，并给出了一些特殊的广义周期环的刻划．

Generalized Periodic Rings

The present paper describes the characterizations of generalized periodic rings and proves that a semiprime generalized periodic ring is either commutative or a direct sum of a nil ring and a P2ring, that is, for any element x there exists an even integer n such that xn=x. A generalized periodic ring with a regular element is proved to be commutative. The present paper also characterizes the rings in which for any elements x and y there exist positive integers m,n of opposite parity such that xm=xn, and shows that if the above condition is satisfied by the ad joint semigroup of a ring R then R is a direct sum of a nil ring and a p2-ring.