MV 代数的子代数及相关重言式之间的关系

摘要

The structures of subalgebras of MV unit interval [0,1] and n-valued MV algebra Ln with the relations of tautolo-gies on them are studied intensively. The main results of this paper are as follows: if a subalgebra M of MV unit interval [0,1] is isomorphism to a subalgebra of MV algebra Ln , then there exists a positive integer m such as (m - 1)|(n - 1) and M = Lm ; if M is a subalgebra of MV unit interval [0,1] , then M is an n-valued MV algebra Ln , or M is a dense subset of [0,1] containing{0,1} ; if positive integer n - 1 can be factored as (m1 - 1)(m2 - 1)(mt - 1) with positive integers m1 - 1,m2 - 1,,mt - 1 rel-atively prime in pairs, then MV algebra Ln can be generated by subalgebras Lm 1,Lm 2,,Lm t; T([0,1]) = n = 2 ¥ T(Ln) , where T(M) is the set of all tautologies on MV-algebra M .%　　对 MV 单位区间[0,1]和 n-值 MV 代数 Ln 的子代数的结构问题及其上重言式之间的关系进行了较为细致的研究。主要结论是：如果 MV 单位区间[0,1]的子代数 M 同构于 n-值 MV 代数 Ln 的子代数,那么,存在正整数 m 满足(m -1)|(n -1)使得 M = Lm ；如果 M 是 MV 单位区间[0,1]的子代数,那么或 M 为有限 MV 代数 Ln ,或 M 为区间[0,1]上包含{0,1}的稠密集；若正整数 n -1可分解为(m1-1)(m2-1)(mt -1),其中 m1-1,m2-1,,mt -1是两两互素的正整数,则 Ln 是 Lm 1,Lm 2,,Lm t生成的 MV 代数；T([0,1])=n =2¥ T(Ln),其中 T(M)表示 MV 代数 M 上全体重言式之集合。