Quantale上的Localic核与Localic余核映射

J4 ›› 2013, Vol. 48 ›› Issue (2): 81-87.

Quantale上的Localic核与Localic余核映射

刘敏, 赵彬*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2012-03-01 出版日期:2013-02-20 发布日期:2013-03-04
通讯作者: 赵彬(1965- ),男,教授,博士生导师,研究方向为格上拓扑与模糊推理. Email:zhaobin@snnu.edu.cn
作者简介:刘敏(1984- ),男,博士研究生,研究方向为格上拓扑学. Email:liumin2010@stu.snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11171196,10871121)

Localic nuclei and conuclei on Quantales

LIU Min, ZHAO Bin*

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2012-03-01 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

研究了Quantale与单位Quantale Q［e］上的Localic核与Localic余核映射。证明了Quantale Q上的Localic核映射可以惟一地扩张为Q［e］上的Localic核映射,双侧的可换Quantale存在最大的Localic子Quantale。再将以上结论应用于研究Quantale Q上的最大的Localic余核映射到Q［e］的扩张,给出了Q上的最大的Localic余核映射到Q［e］的扩张的所有形式,并且证明了Q［e］有最大Localic子Quantale当且仅当Q是平凡Quantale。

关键词: Quantale; Locale;单位Quantale;Quantale 核映射;Quantale 余核映射

Abstract:

This paper deals with localic nuclei and conuclei on quantales and the unital quantale Q［e］. Firstly, it is proved that a localic nucleus on a quantale Q can be uniquely extended to the unital quantale Q［e］. Also, it is proved that a twosided commutative quantale has a largest localic subquantale, which is applied to study the extension of the largest localic quantic conucleus on Q to the unitale quantale Q［e］. All the extensions of a largest localic quantic conucleus to the unitale quantale Q［e］ are given. And it is proved that Q［e］ has a largest localic subquantale if and only if Q is the trivial quantale.

Key words: Quantale; Locale; unital quantale; Quantic nucleus; Quantic conucleus

刘敏, 赵彬*. Quantale上的Localic核与Localic余核映射[J]. J4, 2013, 48(2): 81-87.

LIU Min, ZHAO Bin*. Localic nuclei and conuclei on Quantales[J]. J4, 2013, 48(2): 81-87.

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