R₀-The Generalized Relative Annihilator In Algebra And Its Applications

The theory of filters have great significance for verifying the completeness of the deduction systems in the fuzzy logic.Recently,many scholars have studied the filters in different ways and proposed various forms of filters.As a special class of filters,annihilators are widely used in the research of algebras.Because of their unique operational independence,the R0-algebras as the important kind of algebraic structure have attracted extensive attention of researchers in the filed of non-classical mathematical logic.In order to further reveal their algebraic characteristic,relative annihilators and generalized relative annihilators are proposed and the important properties are studied on the basic of the theories of annihilators in this thesis.The main contributions are follows:1.The concept of relative annihila.tors is introduced and expanded to the gener-alized relative annihilators by merging the characters of filters in the R0-algebra.It is proved that generalized relative annihilators are still filters.Then the relationship between relative annihilators and generalized relative annihilators is studied and the vital properties of the generalized relative annihilator and the related operations of?,? are studied.2.The concepts of fixed filters and relative absorption points are proposed based on the relationship between generalized relative annihilators and filters,and the properties of relative absorption points are mainly discussed to expand the ap-plication range of the generalized relative annihilators.Then,the set of all relative absorption points to the prime filter being a distribution lattice is provided and the prime filters theorem is proved.3.Through the further study of the generalized relative annihilator in the R0-algebras,it is obtained that the completed Heyting algebras are composed by using the generalized relative annihilator based on the given determinants.