计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2015年
2期
60-63,93
,共5页
逻辑代数%MV-代数%?理想%素?理想%同余关系%交互诱导%应用
邏輯代數%MV-代數%?理想%素?理想%同餘關繫%交互誘導%應用
라집대수%MV-대수%?이상%소?이상%동여관계%교호유도%응용
logical algebra%MV-algebra%? ideal%prime ? ideal%congruence relation%alternately deducing%application
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。
在MV-代數中引入瞭?理想概唸，併對?理想與同餘關繫的聯繫及其相關性質進行瞭初步研究。在MV-代數中利用蘊涵算子?給齣瞭?理想的等價錶示形式，進一步揭示瞭?理想與MP濾子的內在聯繫；在MV-代數中研究瞭?理想與同餘關繫之間交互誘導的性質，揭示瞭?理想與同餘關繫的聯繫；利用經典代數的方法證明瞭?理想所誘導的同餘關繫所確定的商代數仍是MV-代數，進而證明瞭通過?理想所決定的商代數是線性MV-代數噹且僅噹?理想是素?理想。
재MV-대수중인입료?이상개념，병대?이상여동여관계적련계급기상관성질진행료초보연구。재MV-대수중이용온함산자?급출료?이상적등개표시형식，진일보게시료?이상여MP려자적내재련계；재MV-대수중연구료?이상여동여관계지간교호유도적성질，게시료?이상여동여관계적련계；이용경전대수적방법증명료?이상소유도적동여관계소학정적상대수잉시MV-대수，진이증명료통과?이상소결정적상대수시선성MV-대수당차부당?이상시소?이상。
The concept of ? ideal is introduced in MV-algebra and the properties and connection of ? ideal and congru-ence 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.
