The structure of principal filters on po-semigroups

The structure of principal filters on po-semigroups

The structure of principal filters on any po-semigroup S is investigated by using the relation Al which is the smallest complete semilattice congruence on S. In particular, we prove that for any po-semigroup S, N. is the equality relation on S if and only if S is a semilattice, and N is the universa...

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Veröffentlicht in:Scientia magna 2006-01, Vol.2 (1), p.50-54
Hauptverfasser: Junzhi, Yan, Xueming, Ren, Siyao, Ma
Format: Artikel
Sprache:eng
Schlagworte:
Congruences and residues
Number theory
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Zusammenfassung:The structure of principal filters on any po-semigroup S is investigated by using the relation Al which is the smallest complete semilattice congruence on S. In particular, we prove that for any po-semigroup S, N. is the equality relation on S if and only if S is a semilattice, and N is the universal relation on S if and only if S is the only principal filter. We also investigate the complete semilattice congruence classes of S.
ISSN:1556-6706