Research Of Morphism And Fuzzy Filter On Effect Algebra

The concept of the effect algebra was introduced as an algebraic structure in1994by American mathematicians Foulis and Bennett. Effect algebra often studies in the case of quantum logic, for example orthomodular lattices and posets. Some concepts and methods about effect algebra are well developed. On the basis of existing literature, we mainly discuss questions concerning the properties of morphism and fuzzy filter on effect algebra and the congruence relation induced by fuzzy filter, and obtain some results.This article is divided into three chapters:In Chapter1, firstly, we introduce some definitions about orthomodular partially ordered set, D-poset and compatibility. Secondly, we give the concept of effect algebra, morphism, etal, and basic properties of effect algebra. Subsequently, several examples about effect algebras are given.In Chapter2, according to the definition of morphism, we discuss its basic properties and obtain some research results. Secondly, we introduce the definition and basic property about monomorphism. And then a relation theorem between lattice homomorphism and monomorphism in lattice effect algebra is obtained. Finally, we introduce a new concept of weak monomorphism, and obtain some equivalent characterizations of weak monomorphism.In Chapter3, in the first section we further studies the properties of the fuzzy filters in effect algebras, which introduce a new concept of normal fuzzy filter, it is discussed a little properties of the normal fuzzy filter. In the second section it discusses the congruence relation of effect algebra induced by fuzzy filter and its properties.