软泛代数及其整体结构性质  

Study on Soft Universal Algebras and Their Global Structure Properties

作　　者：崔靖[1] 徐罗山[2] 

机构地区：[1]泰州职业技术学院基础部,江苏泰州225300 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《模糊系统与数学》2012年第5期67-71,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61074129;61103018);江苏省自然科学基金资助项目(BK2010313;BK2011442)

摘　　要：提出了软泛代数概念,将已有的软群、软环等概念统一纳入这一框架中,从整体上研究了软泛代数的序结构性质,证明了固定指标集和T-代数后,相应的软T-代数全体以点式序形成代数格。引入了Scott连续软泛代数概念,证明了从代数紧拓扑空间到给定T-代数的Scott连续软T-代数的全体以点式序形成代数格。This paper presents the concept of soft universal algebras such that the concepts of soft groups and soft rings are unified in this framework. Order structure properties of soft universal algebras are studied from the whole. It is proved that given an index set and a T-algebra, the corresponding soft T- algebras in the pointwise order forms an algebraic lattice. The concept of Scott continuous soft T-algebras is also introduced and it is proved that all the Scott continuous soft T-algebras from art algebraic compact topological space to a given T-algebra in the pointwise order forms an algebraic lattice.

关 键 词：软泛代数 Scott连续 完备格 代数格 

分 类 号：O141[理学—数学] O153[理学—基础数学]