Order structure of U-semiabundant semigroups and rings Part I: Left Lawson’s order /
In 1991, Lawson introduced three partial orders on reduced Usemiabundant semigroups. Their definitions are formally similar to recently discovered characteristics of the diamond, left star and right star orders respectively on Rickart *-rings; lattice properties of these orders have been studied by...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-019-426-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/73896 |
| Tartalmi kivonat: | In 1991, Lawson introduced three partial orders on reduced Usemiabundant semigroups. Their definitions are formally similar to recently discovered characteristics of the diamond, left star and right star orders respectively on Rickart *-rings; lattice properties of these orders have been studied by several authors. Motivated by these similarities, we turn to the lattice structure of U-semiabundant semigroups and rings under Lawson’s orders. In this paper, we deal with his order 6l on (a version of) right U-semiabundant semigroups and rings. In particular, existence of meets is investigated, it is shown that (under some natural assumptions) every initial section of such a ring is an orthomodular lattice, and explicit descriptions of the corresponding lattice operations are given. |
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| Terjedelem/Fizikai jellemzők: | 359-403 |
| ISSN: | 2064-8316 |