Reverse order law for the inverse along an element

DOI10.1080/03081087.2016.1178209zbMath1379.15004arXiv1512.04875OpenAlexW2298302714MaRDI QIDQ2961461

Pedro Patrício, Huihui Zhu, Jian-Long Chen

Publication date: 20 February 2017

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

Full work available at URL: https://arxiv.org/abs/1512.04875

zbMATH Keywords

semigroupsringsMoore-Penrose inversemonoidreverse order lawinverses along an elementGreen preorders

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Arithmetic theory of semigroups (20M13)

Related Items (15)

Weighted inner inverse for rectangular matrices ⋮ A note on clean elements and inverses along an element ⋮ The one-sided inverse along an element in semigroups and rings ⋮ Reverse order law and forward order law for the (b, c)-inverse ⋮ Outer inverses in semigroups belonging to the prescribed Green's equivalence classes ⋮ On forward-order law for core inverse in rings ⋮ Centralizer's applications to the inverse along an element ⋮ Several characterizations for generalized inverses in a ring ⋮ Further results on several types of generalized inverses ⋮ Absorption laws and reverse order laws for generalized core inverses ⋮ Weighted Moore-Penrose inverses and weighted core inverses in rings with involution ⋮ The existence and expressions of the inverse along operators B and C ⋮ Centralizer's applications to the \((b, c)\)-inverses in rings ⋮ Projections generated by Moore–Penrose inverses and core inverses ⋮ On the (b,c)-inverse in rings

Cites Work

• On generalized inverses and Green's relations
• Drazin-Moore-Penrose invertibility in rings
• Generalized inverses of a factorization in a ring with involution
• On the structure of semigroups
• Further results on the inverse along an element in semigroups and rings
• The inverse along a product and its applications
• Generalized inverses modulo ℋ in semigroups and rings
• Pseudo-Inverses in Associative Rings and Semigroups
• Moore–Penrose invertibility in involutory rings: the case aa ^†=bb ^†

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