否定非对合剩余格的模糊素理想与素模糊理想

Fuzzy Prime and Prime Fuzzy Ideals in Negative Non-involutive Residuated Lattices

对否定非对合剩余格的模糊理想作进一步深入研究.引入否定非对合剩余格模糊素理想和素模糊理想的概念并研究它们的性质和相互关系,获得了模糊素理想和素模糊理想的若干等价刻画,建立了模糊素理想定理和素模糊理想定理.最后,在否定非对合剩余格的全体素模糊理想之集上构造了一个拓扑,证明了相应的拓扑空间是T0空间.所做工作对利用理想概念揭示否定非对合剩余格的代数特征具有一定的促进作用.

The theory of fuzzy ideals in negative non-involutive residuated lattices is deeply studied.The notions fuzzy prime and prime fuzzy ideals in negative non-involutive residuated lattices are introduced and their properties and relation each other are studied.Some characterizations of fuzzy prime and prime fuzzy ideals are given.The fuzzy prime and prime fuzzy ideals theorems are established.Finally,a topology is constructed on the set of all prime fuzzy ideals in a negative non-involutive residuated lattice,it is proved that the topology space is a T 0 space.The results of this paper have a positive role to reveal algebraic features of negative non-involutive residuated lattices by using ideals.