Minimal bi-ideals in regular and completely regular ordered semigroups
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HANSDA, Kalyan. Minimal bi-ideals in regular and completely regular ordered semigroups. In: Quasigroups and Related Systems, 2019, vol. 27, nr. 1(41), pp. 63-72. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 27, Numărul 1(41) / 2019 / ISSN 1561-2848

Minimal bi-ideals in regular and completely regular ordered semigroups

CZU: 512.552.5+512.556
MSC 2010: 20M10, 06F05.

Pag. 63-72

Hansda Kalyan
 
Visva Bharati University
 
 
Disponibil în IBN: 24 august 2019


Rezumat

Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a completely regular ordered semigroup is minimal and hence a regular ordered semigroup S is completely regular if and only if S is union its of minimal bi-ideals.

Cuvinte-cheie
ordered semigroup, Regular, completely regular, bi-ideal, t-simple, ordered idempotents, bi-simple