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Left-star order structure of Rickart *-rings

Insa Krēmere

subject

Ring (mathematics)Algebra and Number TheoryOrder (ring theory)010103 numerical & computational mathematics0102 computer and information sciencesStar (graph theory)01 natural sciencesCombinatoricsSet (abstract data type)Mathematics::LogicOrthogonality010201 computation theory & mathematicsComputer Science::Logic in Computer ScienceMathematics::Category TheoryOrder structure0101 mathematicsMathematics

description

Janowitz proved in 1983 that the initial segments of a Rickart *-ring with the star order are orthomodular posets. In this paper, the same result is proved for the left-star order , which was introduced by Marovtet al., by finding an orthogonality which corresponds to in a certain way and then applying a result proved by Cīrulis which states that the initial segments of any quasi-orthomodular set are orthomodular.

yearjournalcountryeditionlanguage
2015-05-12Linear and Multilinear Algebra
https://doi.org/10.1080/03081087.2015.1040369