On partial orders in Rickart rings

DOI10.1080/03081087.2014.972314zbMath1326.06017OpenAlexW1964632752MaRDI QIDQ2943842

Janko Marovt

Publication date: 4 September 2015

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

Full work available at URL: https://doi.org/10.1080/03081087.2014.972314

zbMATH Keywords

generalized inversespartial ordersstar orderrings with involutionsharp orderRickart ringsminus order

Mathematics Subject Classification ID

Partial orders, general (06A06) Theory of matrix inversion and generalized inverses (15A09) Banach lattices (46B42) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Ordered rings, algebras, modules (06F25)

Related Items (17)

The structures and properties of some generalized invertible operators ⋮ On star, sharp, core, and minus partial orders in Rickart rings ⋮ Unnamed Item ⋮ Weighted pre-orders in a Banach algebra ⋮ On some generalized inverses and partial orders in ∗-rings ⋮ 1MP and MP1 inverses and one-sided star orders in a ring with involution ⋮ On a generalized concept of order relations on B(H) ⋮ Further Results on the Sharp Ordering in Rings ⋮ On sets of elements in Rickart rings induced by partial orders ⋮ Orders in rings based on the core-nilpotent decomposition ⋮ Extending the star order to Rickart rings ⋮ Minus partial order and linear preservers ⋮ Partial orders on the power sets of Baer rings ⋮ On some partial orders on a certain subset of the power set of rings ⋮ Generalization of sharp and core partial order using annihilators ⋮ Partial orders on \(\mathcal{B}(\mathcal{H})\) ⋮ On some orders in ∗-rings based on the core-EP decomposition

Cites Work

• Star partial order on \(B(H)\)
• Matrix partial orders through generalized inverses: Unified theory
• Left-star and right-star partial orderings
• Automorphisms of \(B(H)\) with respect to minus partial order
• On group inverses and the sharp order
• A note on the group structure of unit regular ring elements
• Remarks on the sharp partial order and the ordering of squares of matrices
• On the group-inverse of a linear transformation
• Star, left-star, and right-star partial orders in Rickart ∗-rings
• A note on the star order in Hilbert spaces
• The natural partial order on a regular semigroup
• Natural structures on semigroups with involution
• The diamond partial order in rings

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