Characterizations of core and dual core inverses in rings with involution

DOI10.1080/03081087.2017.1320963zbMath1392.15008arXiv1609.03789OpenAlexW2963726760MaRDI QIDQ4640085

Ting-Ting Li, Jian-Long Chen

Publication date: 16 May 2018

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03789

zbMATH Keywords

ringMoore-Penrose inverseinvolutiongroup inversevon Neumann regularitycore inversedual core inverse

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Units, groups of units (associative rings and algebras) (16U60)

Related Items (25)

A new class of generalized inverses in semigroups and rings with involution ⋮ Projections for generalized inverses ⋮ Three limit representations of the core-EP inverse ⋮ Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse ⋮ Characterizations of weighted core inverses in rings with involution ⋮ Characterizations of the weighted core-EP inverses ⋮ Further results on weighted core inverse in a ring ⋮ Outer inverses in semigroups belonging to the prescribed Green's equivalence classes ⋮ The absorption laws for the weighted core inverse in rings ⋮ One-sided w-core inverses in rings with an involution ⋮ Further results on weighted core-EP inverse of matrices ⋮ The weak group matrix ⋮ Reducible solution to a quaternion tensor equation ⋮ The \((b, c)\)-inverse in semigroups and rings with involution ⋮ Right core inverses of a product and a companion matrix ⋮ The group inverse and core inverse of sums of two elements in a ring ⋮ Weighted Moore-Penrose inverses and weighted core inverses in rings with involution ⋮ The core invertibility of a companion matrix and a Hankel matrix ⋮ The pseudo core inverse of a lower triangular matrix ⋮ Right core inverse and the related generalized inverses ⋮ The core and dual core inverse of a morphism with kernel ⋮ The core inverses of linear combinations of two core invertible matrices ⋮ Core and dual core inverses of a sum of morphisms ⋮ Pseudo core inverses of a sum of morphisms ⋮ Additive properties for the pseudo core inverse of morphisms in an additive category

Cites Work

• On generalized inverses and Green's relations
• Group, Moore-Penrose, core and dual core inverse in rings with involution
• Block generalized inverses
• A note on the group structure of unit regular ring elements
• New characterizations for core inverses in rings with involution
• Drazin-Moore-Penrose invertibility in rings
• Further results on the inverse along an element in semigroups and rings
• Moore–Penrose invertibility in involutory rings: the case aa ^†=bb ^†
• Core inverse of matrices
• Common operator properties of the linear operators 𝑅𝑆 and 𝑆𝑅
• Characterizations and Representations of Core and Dual Core Inverses
• On the algebraic closure in rings
• Core–EP inverse
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