International Journal of Nonlinear Analysis and Applications

Principally π-Baer rings

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science, Shahed University, Tehran, Iran

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

Abstract

We say a ring is right principally $\pi$-Baer (or simply right $p.\pi$-Baer) if an idempotent generates the right annihilator of every projection invariant principal left ideal. The class of right $p.\pi$-Baer rings includes the von Neumann regular rings (and hence right p.p-rings) and all $\pi$-Baer rings. This class of rings is closed under direct products. The behavior of the right $p.\pi$-Baer condition is investigated concerning various constructions and extensions. Moreover, we extend a theorem of Kist for commutative p.p-rings to right $p.\pi$-Baer rings for which every prime ideal contains a unique minimal prime ideal without using topological arguments.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 09 April 2025
  • Receive Date: 14 July 2024
  • Accept Date: 02 December 2024