MV代数的子代数及相关重言式之间的关系

Structure of subalgebra of MV-algebra with relations between tautologies on them

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Lm1,Lm2,…,Lmt生成的MV代数;T([0,1])=∞∩n=2T(Ln),其中T(M)表示MV代数M上全体重言式之集合。

Abstract： The structures of subalgebras of MV unit interval [0, 1] and n-valued MV algebra Ln with the relations of tautologies 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 （mI - 1）（m2 - 1）…（mt - 1） with positive integers rn1 - 1, m2 - 1, …, mt - 1 rel- ao atively prime in pairs, then MV algebra Ln can be generated by subalgebras Lm1, Lm2, …, Lm, ; T（[0, 1]） = ∩ T（Ln）, where n=2 T（M） is the set of all tautologies on MV-algebra M.