%0 Journal Article
%T A class of J-quasipolar rings
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Halicioglu, S.
%A Calci, M. B.
%A Harmanci, A.
%D 2015
%\ 12/01/2015
%V 3
%N 2
%P 1-15
%! A class of J-quasipolar rings
%K Quasipolar ring
%K $J$-quasipolar ring
%K weakly $J$-quasipolar ring
%K uniquely clean ring
%R
%X In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {\it weakly $J$-quasipolar} if there exists $p^2 = p\in comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {\it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investigate general properties of weakly $J$-quasipolar rings. If $R$ is a weakly $J$-quasipolar ring, then we show that (1) $R/J(R)$ is weakly $J$-quasipolar, (2) $R/J(R)$ is commutative, (3) $R/J(R)$ is reduced. We use weakly $J$-quasipolar rings to obtain more results for $J$-quasipolar rings. We prove that the class of weakly $J$-quasipolar rings lies between the class of $J$-quasipolar rings and the class of quasipolar rings. Among others it is shown that a ring $R$ is abelian weakly $J$-quasipolar if and only if $R$ is uniquely clean.
%U https://jart.guilan.ac.ir/article_1537_d40640a41f82ff681c817e78291f88e6.pdf