计算机工程与应用 ›› 2015, Vol. 51 ›› Issue (2): 60-63.

• 理论研究、研发设计 • 上一篇    下一篇

MV-代数中的⊕理想与同余关系及其相关性质

文贤红,吴洪博   

  1. 陕西师范大学 数学与信息科学学院,西安 710062
  • 出版日期:2015-01-15 发布日期:2015-01-12

Properties and connection of [⊕] ideal and congruence relation in MV-algebras

WEN Xianhong, WU Hongbo   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2015-01-15 Published:2015-01-12

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

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