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Turkish Journal of Mathematics
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Extensions of quasipolar rings

Authors: Gurgun, Orhan;

Extensions of quasipolar rings

Abstract

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $��$-regular elements by using quasipolar general rings. We see that quasipolar general rings lies between strongly $��$-regular and strongly clean general rings. Consequently, we prove that $R$ is pseudopolar if and only if $R$ is strongly $��$-rad clean and quasipolar.

18 pages

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Keywords

pseudopolar rings, (generalized) Drazin inverse, strongly clean general, Extensions of associative rings by ideals, quasipolar general rings, Mathematics - Rings and Algebras, Conditions on elements, strongly \(\pi\)-regular general rings, Rings and Algebras (math.RA), FOS: Mathematics, Theory of matrix inversion and generalized inverses, 16S70, 16U99, 15A09

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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