Quantale上的预核映射与预理想余核映射  

The pre-nuclei and pre-ideal conuclei mappings on Quantales

作　　者：孙鹏娟[1] 赵彬[1] 

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：《陕西师范大学学报（自然科学版）》2011年第5期1-6,共6页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871121;11001158)

摘　　要：在Quantale中引入预(左、右)核映射与预(左、右)理想余核映射的概念,讨论了它们的若干性质,建立了预核映射与Quantale商的关系和预理想余核与理想的关系;探讨了预核映射与预理想余核映射到单位Quantale与Girard Quantale的扩张等问题;在预Girard Quantale中,预核映射之集与预理想余核映射之集的对偶是完备格同构.The definitions of pre-（resp.left,right） nuclei mappings and pre-（resp.left,right） ideal conuclei mappings on Quantales are introduced,the relative properties of pre-nuclei and pre-ideal conuclei mappings are proved.The relations among pre-nuclei mappings and quantic quotients,pre-ideal conuclei and ideal are constructed,respectively.The extensions of the pre-nuclei and pre-ideal conuclei mappings to unital Quantale and Girard Quantales are given.It is proved that the set of pre-nuclei mappings and the duality of the set of pre-ideal conuclei mappings are sup-lattice isomorphic.

关 键 词：QUANTALE 预核映射 预理想余核映射 完备格同构 

分 类 号：O153.1[理学—数学]