In this paper we introduce fuzzy congruence and fuzzy strong congruence of semi-hypergroups as well as polygroups. We obtain some results in this respect. We also prove that FC(H), the set of all fuzzy strong congruences on a polygroup H, consists a complete lattice and this lattice is isomorphic to FN (H), the lattice of fuzzy normal subpolygroups.
Reprints available directly from the publisher Published by license under the OCP Science imprint, Photocopying permitted by license only a member of the Old City Publishing Group. We introduce and study fundamental relation of fuzzy hypersemigroups. Also we introduce the notion of a complete part of a fuzzy hypersemi-group and investigate its basic… (More)
The purpose of this paper is the study of congruence and strong congruence of multialgebras. In this regard first we introduce the notion of compatibility and strong compatibility in multialgebras and then we study congruences on multialgebras as a generalization of congruences in ordinary algebras. We investigate some of the important properties of… (More)
Let L be a complete lattice. We introduce and characterize the prime L-submodules of a unitary module over a commutative ring with identity. Finally, we investigate the Zariski topology on the prime L-Spectrum of a unitary module, consisting of the collection of all prime L-submodules, and prove that for L-top modules the Zariski topology on L-Spec(M)… (More)