模糊Quantale范畴中的投射对象  

The projective objects in the category of fuzzy quantales

作　　者：鲁静[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2015年第2期47-54,共8页Journal of Shandong University(Natural Science)

基　　金：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)

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。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.

关 键 词：模糊完全分配格 模糊弱X-稳定完全分配格 投射对象 

分 类 号：O153.1[理学—数学]