半群上的模糊群同余(英文)

Fuzzy Group Congruences on a Semigroup

设 S是一个半群 ,ρ是 S上的一个模糊同余。引进半群的模糊半正规子半群的概念 ,证明ρ是 S上的一个模糊群同余当且仅当它的模糊核 K(ρ)是 S的模糊半正规子半群 ;而且对每个给定的模糊半正规子半群 μ可以构造一个模糊同余 ρμ 使得它的模糊核 K(ρμ) =μ.

Let S be a semigroup and ρ a fuzzy congruence on S. In this paper we introduce the concept of fuzzy seminormal subsemigroup of S, and show that if ρ is a fuzzy group congruence, then its fuzzy kernel K(ρ) is a fuzzy seminormal ubsemigroup of S. Moreover, for every fuzzy seminormal subsemigroup μ of S we can construct a fuzzy group congruence ρ μ on S such that μ=K(ρ μ ).