Focal Baer semigroups and a restricted star order

Cīrulis, Jānis: Focal Baer semigroups and a restricted star order. In: Acta scientiarum mathematicarum, (85) 1-2. pp. 97-117. (2019)

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Abstract

The goal of the paper is to transfer some order properties of starordered Rickart *-rings to Baer semigroups. A focal Baer semigroup S is a semigroup with 0 expanded by two unary idempotent-valued operations, 8 and , such that the left (right) ideal generated by x 8 (resp., x ) is the left (resp., right) annihilator of x. S is said to be symmetric if the ranges of the two operations coincide and p 8 = p for every p from the common range P. Such a semigroup is shown to be P-semiabundant. If it is also Lawson reduced, then P is an orthomodular lattice under the standard order of idempotents, and a restricted version of Drazin star partial order can be defined on S. The lattice structure of S under this order is shown to be similar, in several respects, to that of star-ordered Rickart *-rings.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
ISSN: 2064-8316
Page Range: pp. 97-117
Official URL: http://www.acta.hu
DOI: https://doi.org/10.14232/actasm-017-319-5
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 116-117. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 25. 10:03
Last Modified: 2019. Sep. 25. 10:03
URI: http://acta.bibl.u-szeged.hu/id/eprint/62135

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