Quantale上的预核映射与预理想余核映射

摘要

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.%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.