子Z-Quantale及其性质
Sub-Z-Quantales and their properties
王玲 1赵彬1
作者信息
- 1. 陕西师范大学数学与统计学院,陕西西安 710119
- 折叠
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.
Abstract
Firstly,the concept of the sub-Z-Quantales is introduced and some properties of sub-Z-Quantales are studied.In particu-lar,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-Z-Quantale of a Z-Quantale with a maximum(minimum)element has a maximum(minimum)element.Finally,the concept of conu-clei 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 corre-spondence.
关键词
Z-Quantale/子Z-Quantale/余核映射Key words
Z-Quantale/sub-Z-Quantale/conucleus引用本文复制引用
基金项目
国家自然科学基金资助项目(12101383)
出版年
2024
NETL
NSTL
万方数据