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RESEARCH PRODUCT

The diamond partial order for strong Rickart rings

Jānis Cīrulis

subject

Algebra and Number TheoryMathematics::Rings and Algebras010102 general mathematicsPreorderOrder (ring theory)JoinsDiamondContext (language use)010103 numerical & computational mathematicsState (functional analysis)engineering.materialStar (graph theory)Space (mathematics)01 natural sciencesCombinatoricsengineering0101 mathematicsMathematics

description

The diamond partial order has been first introduced for matrices, and then discussed also in the general context of *-regular rings. We extend this notion to Rickart rings, and state various properties of the diamond order living on the so-called strong Rickart rings. In particular, it is compared with the weak space preorder and the star order; also existence of certain meets and joins under diamond order is discussed.

yearjournalcountryeditionlanguage
2016-05-02Linear and Multilinear Algebra
https://doi.org/10.1080/03081087.2016.1179250