The diamond partial order in rings

DOI10.1080/03081087.2013.779272zbMath1301.06044OpenAlexW2050278490MaRDI QIDQ5409965

Leila Lebtahi, Pedro Patrício, Nestor Janier Thome

Publication date: 15 April 2014

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

Full work available at URL: http://hdl.handle.net/10251/60194

zbMATH Keywords

ringprincipal idealstar partial ordersharp partial orderminus partial order

Mathematics Subject Classification ID

Partial orders, general (06A06) Ordered rings, algebras, modules (06F25)

Related Items (28)

Some new results on the core partial order ⋮ Maps preserving the truncation of products of operators ⋮ Star, left-star, and right-star partial orders in Rickart ∗-rings ⋮ On partial orders in Rickart rings ⋮ On some generalized inverses and partial orders in ∗-rings ⋮ On partial orders of operators ⋮ Convergence of bounded sequences in Hilbert \(C^* \)-modules ⋮ Left and right \(w\)-core partial orders in rings ⋮ Relatively orthocomplemented skew nearlattices in Rickart rings ⋮ 1MP and MP1 inverses and one-sided star orders in a ring with involution ⋮ Partial orders based on core-nilpotent decomposition ⋮ A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore-Penrose inverse ⋮ The diamond partial order for strong Rickart rings ⋮ Moore-Penrose inverse and partial orders on Hilbert space operators ⋮ Partial orders based on the CS decomposition ⋮ Maps preserving the diamond partial order ⋮ Some orders for operators on Hilbert spaces ⋮ Relationships between DMP relation and some partial orders ⋮ On sets of elements in Rickart rings induced by partial orders ⋮ A partial order on the set of complex matrices with index one ⋮ Minus partial order and linear preservers ⋮ Partial orders in rings based on generalized inverses -- unified theory. ⋮ New matrix partial order based on spectrally orthogonal matrix decomposition ⋮ Left and right generalized Drazin invertible operators on Banach spaces and applications ⋮ Ordered matrices with nonnegative group projector ⋮ Bounds for the diamond partial order in ℬ(ℋ) ⋮ Several types of one-sided partial orders in rings ⋮ Core partial order in rings with involution

Cites Work

• Invertibility of a linear combination of two matrices and partial orderings
• Some results on the reverse order law in rings with involution
• Further results on the reverse order law for the Moore-Penrose inverse in rings with involution
• A further algebraic version of Cochran's theorem and matrix partial orderings
• Further results on generalized and hypergeneralized projectors
• Further properties of the star, left-star, right-star, and minus partial orderings.
• Moore–Penrose invertibility in involutory rings: the case aa ^†=bb ^†
• Shorted Operators Relative to a Partial Order in a Regular Ring
• Inter- and extrapolatory properties of matrix partial orderings

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