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arXiv · 1506.08466

A Generalization of $J$-Quasipolar Rings

T. Pekacar Calci·S. Halicioglu·A. Harmanci
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Abstract

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 $p^2 = p\in comm^2(a)$ such that $a + p$ is contained in $\delta(R)$, and the ring $R$ is called {\it $\delta$-quasipolar} if every element of $R$ is $\delta$-quasipolar. We use $\delta$-quasipolar rings to extend some results of $J$-quasipolar rings. Then some of the main results of $J$-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of $\delta$-quasipolar rings.

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T. Pekacar Calci, S. Halicioglu, A. Harmanci. 2015-06-28. A Generalization of $J$-Quasipolar Rings. https://doi.org/10.18514/mmn.2017.1508

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