A Generalization of $J$-Quasipolar Rings

In this paper, we introduce a class of quasipolar rings which is a generalization of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a\in R$ is called {\it $\delta$-quasipolar} if there exists $p^2 = p\in comm^2(a)$suchthat$a + p$iscontainedin$\delta®$,andthering$Ris called {\it\delta-quasipolar} if every element ofR$is$\delta$-quasipolar\mathrm{.}Weuse$\delta$-quasipolarringstoextendsomeresultsof$J$-quasipolarrings\mathrm{.}Thensomeofthemainresultsof$J$-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of $\delta$-quasipolar rings.