Pseudo-Inverses in Associative Rings and Semigroups

1958/08/01 by M. P. Drazin, Michael P. Drazin · 29 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Topics in Algebra #Rings, Modules, and Algebras

paper · doi:10.1080/00029890.1958.11991949

Abstract

(1958). Pseudo-Inverses in Associative Rings and Semigroups. The American Mathematical Monthly: Vol. 65, No. 7, pp. 506-514.

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• Common properties among various generalized inverses and constrained binary relations
• Weighted pseudo core inverses in rings
• One sided polarity along two elements in rings
• Efficiently computing the Uhlmann fidelity for density matrices
• A Drazin inverse for rectangular matrices
• Left and right generalized inverses
• The Drazin inverse in multibody system dynamics
• On the Drazin Index of an Anti-Triangular Block Matrix
• Pseudo core inverses in rings with involution
• Path integral distance for data interpretation
• Characterization and Representation of Weighted Core Inverse of Matrices
• Electron Shuttle Waiting Times for Electric Field Sensing
• Synchronization of thermodynamically consistent stochastic phase oscillators
• On Koliha-Drazin invertible operators and Browder type theorems
• Additive Property of Drazin Invertibility of Elements
• Revisiting generalized inverses of a sum with a radical element
• A new characterization of generalized Browder's theorem and a Cline's formula for generalized Drazin-meromorphic inverses
• Unit Consistency, Generalized Inverses, and Effective System Design Methods
• P-canonical forms and Drazin inverses
• Cramer's Rule for Generalized Inverse Solutions of Some Matrices Equations
• New characterizations for core inverses in rings with involution
• One-sided (b, c)-inverses in rings
• New characterizations of weak CMP inverses
• *-DMP elements in *-semigroups and *-rings
• Drazin Invertibility of Product and Difference of Idempotents in a Ring
• T-Jordan Canonical Form and T-Drazin Inverse based on the T-Product
• Characterizations of weighted (b,c) inverse
• Additive properties and absorption laws for generalized inverses
• Generalized Browder's and Weyl's Theorems for Generalized Derivations

Related

• Introduction to inverse semigroups
• Primer on inverse semigroups I
• Primer on inverse semigroups II
• Natural generalized inverse and core of an element in semigroups, rings and Banach and Operator Algebras
• On Double Inverse Semigroups