The one-sided inverse along an element in semigroups and rings

DOI10.1007/s00009-017-1017-4zbMath1378.15002OpenAlexW2758602044MaRDI QIDQ1679434

Honglin Zou, Huihui Zhu, Pedro Patrício, Jian-Long Chen

Publication date: 9 November 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1822/50142

zbMATH Keywords

semigroupsringsMoore-Penrose inversevon Neumann regularitymonoidcore inverseinverse along an element

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Semigroups (20M99) Associative rings and algebras with additional structure (16W99)

Related Items

Left and right G-outer inverses ⋮ Weighted inner inverse for rectangular matrices ⋮ Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations ⋮ Outer inverses in semigroups belonging to the prescribed Green's equivalence classes ⋮ Left \(w\)-core inverses in rings with involution ⋮ The \((b, c)\)-inverse in semigroups and rings with involution ⋮ The characterizations of one-sided generalized inverses ⋮ Right core inverse and the related generalized inverses

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• Characterizations and representations of the inverse along an element
• The inverse along a lower triangular matrix
• On the structure of semigroups
• Further results on the inverse along an element in semigroups and rings
• The inverse along an element in rings
• Generalized inverses modulo ℋ in semigroups and rings
• Reverse order law for the inverse along an element
• The inverse along an element in rings with an involution, Banach algebras and -algebras
• Pseudo-Inverses in Associative Rings and Semigroups
• Core inverse of matrices
• Elements of rings with equal spectral idempotents
• Characterizations and Representations of Core and Dual Core Inverses
• The Moore-Penrose inverse of von Neumann regular matrices over a ring