Quantale上的预核映射与预理想余核映射-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

Quantale上的预核映射与预理想余核映射

孙鹏娟，赵彬*

(陕西师范大学数学与信息科学学院，陕西西安 710062)

孙鹏娟，女，硕士研究生，研究方向为格上拓扑与模糊推理.Email:pengjuansun@stu.snnu.edu.cn.

摘要:

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.

关键词：

Quantale; 预核映射; 预理想余核映射; 完备格同构

收稿日期：

2011-05-13

中图分类号：

O153.1

文献标识码：

文章编号：

16724291(2011)05000106

基金项目：

国家自然科学基金资助项目(10871121，11001158).

Doi:

The prenuclei and preideal conuclei mappings on Quantales

SUN Pengjuan， ZHAO Bin*

(College of Mathematics and Information Science， Shaanxi Normal University， Xi′an 710062， Shaanxi， China)

Abstract:

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.

KeyWords:

Quantale; prenuclei mappings; preideal conuclei mappings; suplattice isomorphism