TY - JOUR
ID - 1537
TI - A class of J-quasipolar rings
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Halicioglu, S.
AU - Calci, M. B.
AU - Harmanci, A.
AD - Ankara University
AD - Hacettepe University
Y1 - 2015
PY - 2015
VL - 3
IS - 2
SP - 1
EP - 15
KW - Quasipolar ring
KW - $J$-quasipolar ring
KW - weakly $J$-quasipolar ring
KW - uniquely clean ring
DO -
N2 - 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.
UR - https://jart.guilan.ac.ir/article_1537.html
L1 - https://jart.guilan.ac.ir/article_1537_d40640a41f82ff681c817e78291f88e6.pdf
ER -