- Tytuł:
- Ordered Regular Semigroups with Biggest Associates
- Autorzy:
-
Blyth, T.S.
Almeida Santos, M.H. - Tematy:
-
regular semigroup
biggest associate
principally ordered
naturally ordered - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/55790795.pdf Link otwiera się w nowym oknie
- Opis:
- We investigate the class BA of ordered regular semigroups in which each element has a biggest associate x† = max {y | xyx = x}. This class properly contains the class PO of principally ordered regular semigroups (in which there exists x* = max {y | xyx ⩽x}) and is properly contained in the class BI of ordered regular semigroups in which each element has a biggest inverse xo. We show that several basic properties of the unary operation x ↦ x* in PO extend to corresponding properties of the unary operation x ↦ x† in BA. We consider naturally ordered semigroups in BA and prove that those that are orthodox contain a biggest idempotent. We determine the structure of some such semigroups in terms of a principal left ideal and a principal right ideal. We also characterise the completely simple members of BA. Finally, we consider the naturally ordered semigroups in BA that do not have a biggest idempotent.
- Dostawca treści:
- Biblioteka Nauki
Artykuł