模糊Quantale范畴中的投射对象

doi:10.6040/j.issn.1671-9352.0.2014.207

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 47-54.doi: 10.6040/j.issn.1671-9352.0.2014.207

模糊Quantale范畴中的投射对象

鲁静, 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:2014-05-08 修回日期:2014-11-03 出版日期:2015-02-20 发布日期:2015-01-27
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. E-mail:zhaobin@snnu.edu.cn E-mail:zhaobin@snnu.edu.cn
作者简介:鲁静(1989-), 女, 硕士研究生, 研究方向为格上拓扑与模糊推理. E-mail:lujing@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11171196,11301316); 中央高校基本科研业务费专项资金项目(GK201302003)

The projective objects in the category of fuzzy quantales

LU Jing, ZHAO Bin

School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China

Received:2014-05-08 Revised:2014-11-03 Online:2015-02-20 Published:2015-01-27

摘要/Abstract

摘要： 引入了模糊弱⊗-稳定完全分配格的概念, 证明了模糊序半群的下集格带有合适的 ⊗ 运算是模糊弱⊗-稳定完全分配格, 给出了模糊Quantale是模糊弱⊗-稳定完全分配格的充要条件; 讨论了模糊Quantale中的投射对象, 证明了模糊Quantale中的E-投射对象恰是模糊弱⊗-稳定完全分配格.

关键词: -稳定完全分配格, 模糊完全分配格, 模糊弱&otimes, 投射对象

Abstract: The concept of fuzzy weakly ⊗-stable completely distributive lattices is introduced. It is proved that the family of all down sets of a fuzzy ordered semigroup with a appropriate operation ⊗ is a fuzzy weakly ⊗-stable completely distributive lattice. A necessary and sufficient condition for a fuzzy completely distributive lattice to be a fuzzy weakly ⊗-stable completely distributive lattice is given. Finally, projective objects in the category of fuzzy quantales are studied. It is also proved that the E-projective objects in the category of fuzzy quantales are exactly the fuzzy weakly ⊗-stable completely distributive lattices.

Key words: -stable completely distributive lattice, fuzzy completely distributive lattice, projective object, fuzzy weakly ⊗

中图分类号:

O153.1

鲁静, 赵彬. 模糊Quantale范畴中的投射对象[J]. 山东大学学报（理学版）, 2015, 50(02): 47-54.

LU Jing, ZHAO Bin. The projective objects in the category of fuzzy quantales[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 47-54.

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模糊Quantale范畴中的投射对象

The projective objects in the category of fuzzy quantales

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