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EXTENSIONS OF STRONGLY π-REGULAR RINGS

  • Chen, Huanyin ;
  • Kose, Handan ;
  • Kurtulmaz, Yosum
  • Received : 2013.01.07
  • Published : 2014.03.31

Abstract

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

Keywords

strongly ${\pi}$-regular ideal;B-ideal;periodic ideal

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