EXTENSIONS OF STRONGLY pi-REGULAR RINGS

Abstract

An ideal I of a ring R is strongly pi-regular if for any x is an element of I there exist n is an element of N and y is an element of I such that x(n) x(n+l)y. We prove that every strongly pi-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any x is an element of I there exist two distinct m, n is an element of N such that x(m) = x(n). Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly pi-regular and for any u is an element of U(I), u(-1) is an element of Z[u].