@article {
author = {Halicioglu, S. and Calci, M. B. and Harmanci, A.},
title = {A class of J-quasipolar rings},
journal = {Journal of Algebra and Related Topics},
volume = {3},
number = {2},
pages = {1-15},
year = {2015},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {},
abstract = {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.},
keywords = {Quasipolar ring,$J$-quasipolar ring,weakly $J$-quasipolar ring,uniquely clean ring},
url = {https://jart.guilan.ac.ir/article_1537.html},
eprint = {https://jart.guilan.ac.ir/article_1537_d40640a41f82ff681c817e78291f88e6.pdf}
}