Pseudo Drazin inverses in associative rings and Banach algebras

By Zhou Wang, Jianlong Chen. 2012

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Abstract Motivated by strongly π -regular elements and quasipolar elements, we introduce the concept of pseudopolar elements. An element a ∈ R is called pseudopolar if there exists p ∈ R such that p 2 = p ∈ comm 2 ( a ) , a + p ∈ U ( R ) and a k p ∈ J ( R ) for some positive integer k. This concept can be used exactly to define a pseudo Drazin inverse in associative rings and Banach algebras. We connect pseudopolar rings with strongly π -regular rings, semiregular rings, uniquely strongly clean rings and uniquely bleached local rings. Some basic properties of pseudo Drazin inverses are obtained in associative rings and Banach algebras.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/712c419aa42258c27c1af0e189fd7904bdf3c0f5