Z-Quantale的表示定理  

Representation Theorems for Z-Quantales

作　　者：杜佳慧 刘敏[1] DU Jiahui;LIU Min(School of Sciences,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《吉林大学学报（理学版）》2021年第6期1368-1374,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11871320).

摘　　要：考虑Z-Quantale的表示问题.首先,证明任意单位Z-Quantale都同构于由其强Z-自连续映射所构成的Z-Quantale;其次,证明对于任意单位Z-Quantale都存在其上的一个关系Z-Quantale与其同构;最后,讨论单位Z-Quantale范畴与关系Z-Quantale范畴之间的关系,证明单位Z-Quantale范畴与关系Z-Quantale范畴等价.We considered representation problems of Z-Quantales.Firstly,we proved that any unital Z-Quantale was isomorphic to the Z-Quantale formed by its strong self-continuous maps.Secondly,we proved that any unital Z-Quantale was isomorphic to a relation Z-Quantale.Finally,we discussed the relationship between the category of unital Z-Quantales and the category of relation Z-Quantales,and proved that the category of unital Z-Quantales was equivalent to the category of relation Z-Quantales.

关 键 词：Z-Quantale 单位Z-Quantale Z-Quantale同构 表示定理 

分 类 号：O153.1[理学—数学]