反Heyting代数中MT理想及其性质  

MT Ideals of Inverse Heyting Algebras with Their Characteristic

作　　者：冯丹丹 吴洪博[1] FENG Dan-dan;WU Hong-bo(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《云南师范大学学报（自然科学版）》2019年第3期16-22,共7页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(61572016)

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.

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 

分 类 号：O141.1[理学—数学]