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

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International Electronic Journal of Algebra
Volume:30 Issue:30
$\pi$-BAER $\ast$-RINGS

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

Authors : Ali SHAHIDIKIA, Hamid Haj Seyyed JAVADI, Ahmad MOUSSAVI

Pages : 231-242

Doi:10.24330/ieja.969915

View : 10 | Download : 13

Publication Date : 2021-07-17

Article Type : Research Paper

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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