EXTENSIONS OF STRONGLY π-REGULAR RINGS

Title & Authors
EXTENSIONS OF STRONGLY π-REGULAR RINGS
Chen, Huanyin; Kose, Handan; Kurtulmaz, Yosum;

Abstract
An ideal I of a ring R is strongly $\small{{\pi}}$-regular if for any $\small{x{\in}I}$ there exist $\small{n{\in}\mathbb{N}}$ and $\small{y{\in}I}$ such that $\small{x^n=x^{n+1}y}$. We prove that every strongly $\small{{\pi}}$-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any $\small{x{\in}I}$ there exist two distinct m, $\small{n{\in}\mathbb{N}}$ such that $\small{x^m=x^n}$. Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly $\small{{\pi}}$-regular and for any $\small{u{\in}U(I)}$, $\small{u^{-1}{\in}\mathbb{Z}[u]}$.
Keywords
strongly $\small{{\pi}}$-regular ideal;B-ideal;periodic ideal;
Language
English
Cited by
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