EXTENSIONS OF STRONGLY Π-Regular RINGS

Abstract

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