关键词: 逻辑代数, MV-代数, [&oplus, ]理想, 素[&oplus, ]理想, 同余关系, 交互诱导, 应用

Abstract: The concept of [⊕] ideal is introduced in MV-algebra and the properties and connection of [⊕] ideal and congruence relation in MV-algebras are discussed. The equivalent representation of [⊕] ideal is given by implication operator, and the internal relation between [⊕] ideal and MP-filter is revealed. The properties of alternately deducing between [⊕] ideal and congruence relation of MV-algebras are studied and the connection of [⊕] ideal and congruence relation is clear. It is proved that the quotient algebras deduced by [⊕] ideal in MV-algebra are also MV-algebras by classical algebra’s method. Furthermore, it is proved that the quotient algebra deduced by [⊕] ideal is linear algebra if and only if [⊕] ideal is a prime [⊕] ideal.

Key words: logical algebra, MV-algebra, [⊕]ideal, prime[⊕]ideal, congruence relation, alternately deducing, application