SEMILATTICE CONGRUENCE AND FUZZY SEMILATTICE CONGRUENCE ON PO-Γ-SEMIGROUP VIA ITS OPERATOR SEMIGROUPS

Sujit Kumar Sardar; Pavel Pal; Rajlaxmi Mukherjee

Sujit Kumar Sardar
Pavel Pal
Rajlaxmi Mukherjee

Keywords: po-Γ-semigroup, operator semigroup, semilattice congruence, fuzzy semilattice congruence

Abstract

In this paper, semilattice congruence and fuzzy semilattice congruence on po-Γ-semigroup are studied via operator semigroups. Among other results we obtain a lattice isomorphism between fuzzy semilattice congruences of a Γ-semigroup and that of its left operator semigroup. Using this result we have shown that any sublattice of the lattice of all fuzzy semilattice congruences of a po-Γ-semigroup is modular.