MV-代数中的Å理想与同余关系及其相关性质

摘要

在MV-代数中引入了Å理想概念，并对Å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Å理想的等价表示形式，进一步揭示了Å理想与MP滤子的内在联系；在MV-代数中研究了Å理想与同余关系之间交互诱导的性质，揭示了Å理想与同余关系的联系；利用经典代数的方法证明了Å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Å理想所决定的商代数是线性MV-代数当且仅当Å理想是素Å理想。%The concept of Å ideal is introduced in MV-algebra and the properties and connection of Å ideal and congru-ence relation in MV-algebras are discussed. The equivalent representation of Å ideal is given by implication operator, and the internal relation between Å ideal and MP-filter is revealed. The properties of alternately deducing between Å ideal and congruence relation of MV-algebras are studied and the connection of Å ideal and congruence relation is clear. It is proved that the quotient algebras deduced by Å ideal in MV-algebra are also MV-algebras by classical algebra’s method. Furthermore, it is proved that the quotient algebra deduced by Å ideal is linear algebra if and only if Å ideal is a prime Å ideal.