The Moore-Penrose inverse in rings with involution

Xu, Sanzhang; Chen, Jianlong

doi:10.2298/fil1918791x

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Characterizing Core and Dual Core Inverse Of A Regular Eleme1

Introduction1

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2021

2023

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Cited by 6 publications

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“…Proof. It is obvious that the conditions (1) and (2) are equivalent, and equivalences of the conditions (3), (4), (5) and (6) can be deduced from Lemma 2.6.…”

Section: Characterizing Core and Dual Core Inverse Of A Regular Elemementioning

confidence: 95%

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Characterizations of core and dual core inverses in rings with involution

Chen

2017

Linear and Multilinear Algebra

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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 a ∈ R and n 1, then a is core invertible if and only if there exists a Hermitian element (or a projection) p such that pa = 0, a n + p is invertible. As a consequence, a is an EP element if and only if there exists a Hermitian element (or a projection) p such that pa = ap = 0, a n + p is invertible. We also get a new characterization for both core invertible and dual core invertible of a regular element by units, and their expressions are shown. In particular, we prove that for n 2, a is both Moore-Penrose invertible and group invertible if and only if (a * ) n is invertible along a.

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“…Proof. It is obvious that the conditions (1) and (2) are equivalent, and equivalences of the conditions (3), (4), (5) and (6) can be deduced from Lemma 2.6.…”

Section: Characterizing Core and Dual Core Inverse Of A Regular Elemementioning

confidence: 95%

“…Chen characterized {1, 3}−inverse of an element by projections. In [5], S.Z. Xu et al gave the characterizations and expressions of Moore-Penrose inverse of an element by a Hermitian element (or a projection).…”

Section: Introductionmentioning

confidence: 99%