子Z-Quantale及其性质  

Sub-Z-Quantales and their properties

作　　者：王玲[1] 赵彬[1] WANG Ling;ZHAO Bin(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,Shaanxi,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《山东大学学报（理学版）》2024年第6期76-83,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12101383)。

摘　　要：首先引入子Z-Quantale的概念,研究子Z-Quantale的一些性质。特别地,构造单位Z-Quantale的所有含有单位元的子Z-Quantale集上的二元运算⊙,使得其成为Quantale。其次,定义并子Z-Quantale,证明有最大(小)元的Z-Quantale的并子Z-Quantale一定有最大(小)元。最后,引入Z-Quantale上余核映射的概念,证明Z-Quantale上的并子Z-Quantale与其上的余核映射是一一对应的。Firstly,the concept of the sub-Z-Quantales is introduced and some properties of sub-Z-Quantales are studied.In particular,the binary operation⊙on the set of all sub-Z-Quantales of a unital Z-Quantale containing the identity element is constructed such that the set is a Quantale.Secondly,the definition of join sub-Z-Quantales is given,and it is proved that every join sub-ZQuantale of a Z-Quantale with a maximum(minimum)element has a maximum(minimum)element.Finally,the concept of conuclei on Z-Quantales is introduced,and it is proved that the join sub-Z-Quantales and conuclei on a Z-Quantale are one-to-one correspondence.

关 键 词：Z-Quantale 子Z-Quantale 余核映射 

分 类 号：O153.1[理学—数学]