剩余格中的素(p)滤子  

Prime(p)Filters of Residual Lattices

作　　者：舒忠平[1] 龚加安[1,2] 崔宏志[1] 吴洪博[2] SHU Zhongping;GONG Jiaan;CUI Hongzhi;WU Hongbo(Shanxi Shangluo Vocation and Technical Institution,Shang luo 726000,Shaanxi China;College of Mathematics and Information Science,Shaanxi Normal University,Xi＇an 710062,China)

机构地区：[1]陕西省商洛职业技术学院,陕西商洛726000 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《河南科学》2018年第10期1501-1504,共4页Henan Science

基　　金：国家自然科学资助项目(NO.11171196);陕西省教育厅科学研究项目(17JK0962);商洛职业技术学院2017年度重大课题(2017JXKT06)

摘　　要：在剩余格中定义了一类特殊的素(p)滤子,讨论了它们的结构和性质.证明了该剩余格中的蕴涵运算可由这些特殊的素(p)滤子所确定,并且这些特殊的素(p)滤子的全体构成一个剩余格,它与原剩余格具有格蕴涵同构关系.当剩余格是MTL代数,IMTL代数,BL代数,MV代数或R0代数时,上述结论也成立.In this paper, aspecial kind of prime （p） filters are defined in a residual lattice, then their structures and properties are discussed. It is proved that the implication operation in the residual lattice is determined by these prime （p） filters, and all of these prime （p） filters compose a residual lattice, which is the same lattice implication isomorphic to the former residual lattice. The conclusion is suit for MTL algebra, IMTL algebra, BL algebra, MV algebra, and R0 algebra.

关 键 词：剩余格 素(p)滤子 格蕴涵同构 

分 类 号：O141[理学—数学]