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

摘要： 在MV-代数中引入了[⊕]理想概念，并对[⊕]理想与同余关系的联系及其相关性质进行了初步研究。在MV-代数中利用蕴涵算子[→]给出了[⊕]理想的等价表示形式，进一步揭示了[⊕]理想与MP滤子的内在联系；在MV-代数中研究了[⊕]理想与同余关系之间交互诱导的性质，揭示了[⊕]理想与同余关系的联系；利用经典代数的方法证明了[⊕]理想所诱导的同余关系所确定的商代数仍是MV-代数，进而证明了通过[⊕]理想所决定的商代数是线性MV-代数当且仅当[⊕]理想是素[⊕]理想。

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