| Quantale theory,closely related to the linear logic and theoretical computer sci-ence,appeared in the 1980s.Not only logicians and theoretical computer scientists,but also mathematicians are attracted because of its abundant algebraic structures and order structures.The sup-algebra,as a concrete extension of quantale,is in-troduced by Resende in 1998.The motivation is to provide a unified framework for studying various quantale-like structures(Frame,Q-modules,S-quantale,etc.).In 1965,Zadeh presented the concept of fuzzy set.Recently,many basic concepts and relative conclusions in classical posets are fuzzed by some scholars with the development of fuzzy set theory,then many excellent research results are gained.In this paper,we study the properties of fuzzy sup-algebra and the injectivity of fuzzy ordered algebra category.The main contents of this thesis are arranged as follows:Chapter One:Preliminaries.In this chapter,some basic knowledge in fuzzy orderd algebra theory and category theory is given,which will be usesd throughout the paper.Chapter Two:The relative properties of fuzzy sup-algebra.Firstly,the con-cept of fuzzy congruence on fuzzy sup-algebra is given,and it is proved that the set of all fuzzy congruences is fuzzy order isomorphic to the set of fuzzy nuclei.Then,the quotient of fuzzy sup-algebra congruences is provided and the corresponding conclu-sions are obtained.Finally,the fuzzy conucleus on fuzzy sup-algebra is introduced and the corresponding relationship with fuzzy sup-subalgebra is studied.Chapter Three:The injective object and injective hull of fuzzy ordered algebra category.Firstly,the injective object in fuzzy ordered algebra category is discussed,and it is proved that an M?-injective object in fuzzy ordered algebra category is exactly fuzzy sup-algebra.Secondly,the form of M?-injective hull of fuzzy ordered algebra satisfying a certain condition is given. |
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