The diamond partial order for strong Rickart rings

DOI10.1080/03081087.2016.1179250zbMath1383.06005OpenAlexW2345346771MaRDI QIDQ2961463

Jānis Cīrulis

Publication date: 20 February 2017

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

Full work available at URL: https://doi.org/10.1080/03081087.2016.1179250

zbMATH Keywords

diamond partial orderRickart \(\ast\)-ringsspace preorderstrong Rickart rings

Mathematics Subject Classification ID

Partial orders, general (06A06) Theory of matrix inversion and generalized inverses (15A09) Abstract operator algebras on Hilbert spaces (47L30) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Ordered rings, algebras, modules (06F25) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (5)

Notes on reduced Rickart rings. I. Representation and equational axiomatizations ⋮ Convergence of bounded sequences in Hilbert \(C^* \)-modules ⋮ Partial orders in non-commutative \(L^p\) spaces associated with semi-finite von Neumann algebras ⋮ Automorphisms on the poset of products of two projections ⋮ Bounds for the diamond partial order in ℬ(ℋ)

Cites Work

• Matrix partial orders through generalized inverses: Unified theory
• On regular rings with involution
• A further algebraic version of Cochran's theorem and matrix partial orderings
• A note on Rickart rings and semi-Boolean algebras
• Star, left-star, and right-star partial orders in Rickart ∗-rings
• Lattice operations on Rickart ∗-rings under the star order
• The diamond partial order in rings
• Extending the star order to Rickart rings

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