自由LF模  

Free Objects in the Category of LF Modules

作　　者：汤建钢[1] 

机构地区：[1]伊犁师范学院

出　　处：《模糊系统与数学》1991年第1期23-26,共4页Fuzzy Systems and Mathematics

摘　　要：本文以范畴理论为工具,讨论了由L F集生成的L F模问题,给出了L F集在L F模范畴中的自由对象的存在性、唯一性、结构性定理。In this paper, we're studied the problems of free objects in the category of LF modules, the main results in the paper are as follows: Theorem 1. Let ((F,B),f) be the free object of LF set (X,A) in the category of LF modules, then 1) (F, f) is the free object of set X in the category of left R-modules; 2) B=<f(A)>; 3) If ((E,C),g) is, too, free object of LF set (X,A) in the category of LF modules if and only if there exists a unigue isomorphism h(?)Hom R-mod(L) ((F,B),(E,C)) such that h(?)f=g. Theorem 2 ((F(X),<i_x(A)>), i_x) is free object of LF set(X,A) in the category of LF modules. 1) F(X)={θ|θ: X→R such that θ(x)=0 for all but a finite number of the x's}; 2) i_x is a map from X to F(X), and i_x(x) is defined by [i_x(x)](x)=I_R, [i_x(x)](y)=0 if y(?)x; 3) <i_x(A)>(θ)=∧{A(x)|x(?)X and θ(x)(?)0}.

关 键 词：LF模范畴 自由LF模 LF集 存在性 唯一性 

分 类 号：O159[理学—数学]