MV - Algebra (~) Ideal And Related Research

In logic algebras, the implication operator is crucial and fundamental in the structure of the logic algebras. After famous logician C.C.Chang proposed MV-algebra. The lattice implication algebra is based on the combination of the char-acteristics of implication in MV-algebra and the bounded lattice. The equivalent representation of ideal is given by implication operator, and the internal relation between (?) ideal and MP-filter is revealed. The properties and the applications of the (?) ideal are discussed. The concepts of the unordered (?) ideal and the prime unordered (?) ideal in the structure are introduced. Moreover, the properties and the generating method of the unordered (?) ideal are studied.The construction of chapters and the concrete contents of this paper are as follows:Chapter1:Preliminaries. we give the basic concepts of lattice, ideal, distribu-tive lattice, MV-algebra, and the properties of ideal in MV-algebra.Chapter2:The characteristics and the in MV-algebra. At first, The equivalent representation of ideal is given; Then, the relation between (?) ideal and common ideal and the characteristics of the (?) ideal are discussed; Finally, the extension of the (?) ideal is studied.Chapter3:The interaction of inducing between the (?) ideal and the congruence relation in MV-algebra. Firstly, the concept of the congruence relation is defined. Secondly, the (?) ideal derived by the congruence relation and the congruence relation derived by the (?) ideal are discussed. Thirdly, the invariability of the (?) ideal and the congruence are derived by each other.Chapter4:The quotient algebra and embedding of MV-algebra. The quotient algebra of MV-algebras is defined with the help of the (?) idea. Then, the equivalent representation of prime (?) ideal is given. Also, it is proved that the quotient alge-bra deduced by prime (?) ideal is linear. Furthermore, the theorem of conditional embedding of MV-algebra is gained.Chapter5:The unordered (?) idea of MV-algebra and its generating method. Firstly, the concept of unordered (?) idea and prime unordered (?) idea of MV-algebra are introduced, and the properties of them are studied. Then, the generating method of the unordered (?) idea is given in MV-algebra.