Prime Fuzzy Ideals Of Quantales And Fuzzy Implicative Filters Of Girard Quantale

Quantale was introduced by C. J.Mulvey in 1986,with the intent of offering a new lattice-characterization for studying noncommutative C*-algebra and a new mathematicial model for quantum mechanics. Since quantale theory provides a powerful tool in studying noncommutative topology, linear logic and C*-algebra theory. For quantale can be regard as the generalization of frame, it has full interior structures.This thesis is to investigate the fuzzy structures of quantales.The structure of this thesis is organized as follows:Chapter One Preliminary knowledge. In this chapter, we give the basic con-cepts and results of the theory of quantale and that of fuzzy mathematics which will be used throughout the thesis.Chapter Two Prime fuzzy ideals of Quantales. Firstly, some properties and conclusions of fuzzy ideals in quantale are given. Secondly, the concept of ordered fuzzy point in quaritale is introduced. There are characterizations of fuzzy ideals of quantale in terms of ordered fuzzy points. Thirdly, we give some properties of prime fuzzy ideals of a quantale.Chapter Three Weakly prime fuzzy ideals and Completely prime fuzzy ideals of Quantales. Firstly, we introduce the concepts of weakly prime fuzzy ideals, completely prime fuzzy ideals, weakly completely prime fuzzy ideals and completely semiprime fuzzy ideals of a quantale. Furthermore, we establish the relationship between some classes of ideals, and characterize weakly prime fuzzy ideals, weakly completely prime fuzzy ideals and completely semiprime fuzzy ideals of quantale by their level ideals. Finally, we introduce the fuzzy radicals of quantales, and prove that the fuzzy radical of every completely semiprime fuzzy ideal of a quantale can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it.Chapter Four Fuzzy implicative filters of Girard Quantale. Firstly, some prop-erties of Girard quantale are given. Secondly, the concepts of fuzzy filter in Girard Quantale is introduced, and its some properties are obtained. Thirdly, we introduce the concept of fuzzy implicative filter in Girard Quantale. The equivalent descrip-tions of fuzzy implicative filter are given,the relation between fuzzy implicative filter and fuzzy Boolean filter is discussed.