Extensions of quasipolar rings
Authors : Orhan GÜRGÜN
Pages : 15-26
View : 10 | Download : 6
Publication Date : 0000-00-00
Article Type : Research Paper
Abstract :An associative ring with identity is called quasipolar provided that for each $a\in R$ there exists an idempotent $p\in R$ such that $p\in comm^2insert ignore into journalissuearticles values(a);$, $a+p\in Uinsert ignore into journalissuearticles values(R);$ and $ap\in R^{qnil}$. In this article, we introduce the notion of quasipolar general rings insert ignore into journalissuearticles values(with or without identity);. Some properties of quasipolar general rings are investigated. We prove that a general ring $I$ is quasipolar if and only if every element $a\in I$ can be written in the form $a=s+q$ where $s$ is strongly regular, $s\in comm^2insert ignore into journalissuearticles values(a);$, $q$ is quasinilpotent, and $sq=qs=0$. It is shown that every ideal of a quasipolar general ring is quasipolar. Particularly, we show that $R$ is pseudopolar if and only if $R$ is strongly $\pi$-rad clean and quasipolar.Keywords : Quasipolar general rings, strongly clean general rings, strongly pi regular general rings generalized, Drazin inverse, pseudopolar rings