Central quasipolar rings

Abstract

In this paper, we introduce a kind of quasipolarity notion for rings, namely, an element a of a ring R is called central quasipolar if there exists p 2 = p ∈ R such that a + p is central in R, and the ring R is called central quasipolar if every element of R is central quasipolar. We give many characterizations and investigate general properties of central quasipolar rings. We determine the conditions that some subrings of upper triangular matrix rings are central quasipolar. A diagonal matrix over a local ring is characterized in terms of being central quasipolar. We prove that the class of central quasipolar rings lies between the classes of commutative rings and Dedekind nite rings, and a ring R is central quasipolar if and only if it is central clean. Further we show that several results of quasipolar rings can be extended to central quasipolar rings in this general setting.