Focal Baer semigroups and a restricted star order
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., r...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-017-319-5 |
| Online Access: | http://acta.bibl.u-szeged.hu/62135 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 97-117 |
| ISSN: | 2064-8316 |