Extensions of quasipolar rings

Abstract

An associative ring with identity is called quasipolar provided that for each a ∈ R there exists an idempotent p ∈ R such that p ∈ comm 2 (a) , a + p ∈ U (R) and ap ∈ R qnil . In this article, we introduce the notion of quasipolar general rings (with or without identity). Some properties of quasipolar general rings are investigated. We prove that a general ring I is quasipolar if and only if every element a ∈ I can be written in the form a = s + q where s is strongly regular, s ∈ comm 2 (a) , q is quasinilpotent, and sq = qs = 0 . It is shown that every ideal of a quasipolar general ring is quasipolar. Particularly, we show that R is pseudopolar if and only if R is strongly π -rad clean and quasipolar.

Determinants of Dollarization of Savings in the Turkish Economy

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