Characterizations of core and dual core inverses in rings with involution

By Tingting Li, Jianlong Chen. 2016

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ABSTRACT Let R be a unital ring with involution. We give the characterizations and representations of the core and dual core inverses of an element in R by Hermitian elements (or projections) and units. For example, let and . Then a is core invertible if and only if there exists a Hermitian element (or a projection) p such that and is invertible. As a consequence, a is an element if and only if there exists a Hermitian element (or a projection) p such that and is invertible. We also get a new characterization for both core invertibility and dual core invertibility of a regular element by units, and their expressions are shown. In particular, we prove that for , a is both Moore–Penrose invertible and group invertible if and only if is invertible along a.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/77ef56e70b1f20e88198da06d83240ebc83f94b1