反Heyting代数中MT理想及其性质

详细信息    查看全文 | 推荐本文 |

英文篇名：MT Ideals of Inverse Heyting Algebras with Their Characteristic 作者：冯丹丹 ; 吴洪博 英文作者：FENG Dan-dan;WU Hong-bo;College of Mathematics and Information Science,Shaanxi Normal University; 关键词：反Heyting代数 ; MT理想 ; 素MT理想 ; 极大MT理想 ; 次极大MT理想 英文关键词：Inverse Heyting algebra;;MT ideal;;Prime MT ideal;;Maximal MT ideal;;Submaximal MT ideal 中文刊名：YNSK 英文刊名：Journal of Yunnan Normal University(Natural Sciences Edition) 机构：陕西师范大学数学与信息科学学院; 出版日期：2019-05-15 出版单位：云南师范大学学报(自然科学版) 年：2019 期：v.39;No.189 基金：国家自然科学基金资助项目(61572016) 语种：中文; 页：YNSK201903005 页数：7 CN：03 ISSN：53-1046/N 分类号：20-26

摘要

将MT理想的概念引入到反Heyting代数中并对其性质进行了较为深入的研究.首先,在反Heyting代数中通过反蕴涵算子提出了MT理想的概念,讨论了MT理想的等价条件和他的基本性质;其次,给出了反Heyting代数的MT理想的几种生成方法;最后,在反Heyting代数中提出了素MT理想、极大MT理想以及次极大MT理想的概念,并且讨论了这些特殊理想的性质以及相互关系.
        The concept of MT ideals is introduced into the inverse Heyting algebras,and the characteristic of MT ideals is discussed deeply.Firstly,in the inverse Heyting algebras,the concept of MT ideals is proposed by the inverse implication operator,and the basic properties and equivalent condition of MT ideals are discussed.Secondly,some generation methods of MT ideals are given in the inverse Heyting algebras.At last,the concept of prime MT ideals,maximal MT ideals and submaximal MT ideals are proposed in the inverse Heyting algebras,and their fundamental properties and relationships among them are studied.

引文

[1] 王国俊.Heyting代数成为Boole代数的条件及其特征[J].陕西师范大学学报,1991,19(4):1-6.
    [2] 吴洪博,石慧君.Heyting系统及其H-Locale化形式[J].数学学报,2012,55(6):1 119-1 130.
    [3] 吴洪博,石慧君.Heyting系统及其H-空间化表现形式[J].电子学报,2012,40(5):995-999.
    [4] VICKERS S.Topology via Logic[M].Cambridge:Cambridge University Press,1989.
    [5] DAVEY B A,PRIESTLEY H A.Introduction to Lattices and Order Second edition[M].Cambridge:Cambridge University Press,1990,2002.
    [6] 刘春辉,徐罗山.关于剩余格的理想[J].山东大学学报:理学版,2010,45(4):66-71.
    [7] DVURE CENSKIJ A,PULMANNOW A S.New trends in quantum structures[M].Dordrecht:Kluwer Academic Publishers,2000.
    [8] 吴洪博,王娜.BR0-代数中MT理想的扩展及素MT理想的存在性[J].电子学报,2015,43(6):1 137-1 143.
    [9] 吴洪博,汪宁.基于正则FI代数的MT理想及其应用[J].电子学报,2013,41(7):1 389-1 394.
    [10] 李国华,汤建钢,张红.完备格中四种蕴涵运算与伴随关系[J].模糊系统与数学,2010,24(6):56-60.
    [11] 郑崇友,樊磊,崔宏斌.Frame与连续格[M].北京:首都师范大学出版社,1994.