$\pi$-BAER $\ast$-RINGS

Year 2021, , 231 - 242, 17.07.2021

Ali Shahıdıkıa Hamid Haj Seyyed Javadı Ahmad Moussavı

https://doi.org/10.24330/ieja.969915

Abstract

A $\ast$-ring
$R$ is called a $\pi$-Baer $\ast$-ring, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y $
is generated, as a right ideal, by a projection.
In this note, we
study some properties of such $\ast$-rings.
We indicate interrelationships between the $\pi$-Baer $\ast$-rings and related classes of rings such as
$\pi$-Baer rings, Baer $\ast$-rings, and quasi-Baer $\ast$-rings. We announce several
results on $\pi$-Baer $\ast$-rings.
We show that this notion is well-behaved with respect to
polynomial extensions and full matrix rings.
Examples are provided to explain and delimit our results.

Keywords

$\pi$-Baer ring, $\pi$-Baer $\ast$-ring, quasi-Baer $\ast$-ring, Baer ring, Baer $\ast$-ring

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