Shorted Operators Relative to a Partial Order in a Regular Ring

DOI10.1080/00927870902828629zbMath1198.06010arXiv1010.0051OpenAlexW2140883797MaRDI QIDQ3653343

K. Manjunatha Prasad, Brian Blackwood, Ashish K. Srivastava, Surender Kumar Jain

Publication date: 22 December 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0051

zbMATH Keywords

partial ordershorted operatorvon Neumann regular ringLoewner order

Mathematics Subject Classification ID

Partial orders, general (06A06) Theory of matrix inversion and generalized inverses (15A09) Ordered rings, algebras, modules (06F25) Topological and ordered rings and modules (16W80) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (16)

Lattice properties of the minus order on regular modules ⋮ Space pre-order and minus partial order for operators on Banach spaces ⋮ A note on the right-left symmetry of aR ⊕ bR = (a + b)R in rings ⋮ Drazin inverse and generalization of core-nilpotent decomposition ⋮ Unit-regularity of elements in rings ⋮ On (unit-)regular morphisms ⋮ Minus partial order in regular modules ⋮ Solving a minus partial ordering equation over von Neumann regular rings. ⋮ The direct sum order in regular modules ⋮ Regular Elements in Quasi-Morphic Rings ⋮ Inverse complements of a matrix and applications ⋮ The diamond partial order in rings ⋮ Solutions of minus partial ordering equations over von Neumann regular rings ⋮ Minus partial order and linear preservers ⋮ Shorted operators with respect to a partial order in a dual module ⋮ Inverse complements and strongly unit regular elements

Cites Work

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• The minus partial order and the shorted matrix
• Shorted operators and generalized inverses of matrices
• Right-left symmetry of \(aR\oplus bR=(a+b)R\) in regular rings
• Über monotone Matrixfunktionen
• The natural partial order on a regular semigroup
• Shorted Operators. II
• Natural structures on semigroups with involution
• Extensions of $\mathcal{G}$-Based Matrix Partial Orders
• Pseudoinverss of Postive Semidefeinite Matrices
• Shorted Operators

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