Abstract:

The definition of L-fuzzy frame is generalized to L-fuzzy quantale, and some equivalent charaterizations of L-fuzzy quantale are given. The concept of L-filter and L-filtered quantale are introduced. It is proved that every L-filter can generate an L-filtered quantale, and there is an honest functor from L-FilQuant to L-FQuant. Finally, the concept of L-fuzzy ideal and L-fuzzy prime ideal are introduced, and their properties are discussed.

Key words: L-fuzzy quantale; L-filter; category; functor; ideal