MV* - Algebras
MV* - Algebras
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DOI：
10.1093/jigpal/12.6.461
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Renato A. Lewin;M. Sagastume;P. Massey
中科院分区：
文献类型：
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作者：
Renato A. Lewin;M. Sagastume;P. Massey
本文对C. C. Chang作为具有正负真值逻辑的代数对应物。我们建立了代数理论MV*-代数在其自身的限制使用的概念，理想和素理想是非常自然地相关的相应概念，在l-群。主要结果是一个次直接表示定理，一个完整性定理，研究简单和半简单代数，和表征理想的无穷小作为一个l-群。在最后一节中，我们详细证明了McNaughton的一维定理，即在一个生成元中的自由MV*-代数是[-1，1]上的McNaughton函数的代数。与其余的文件相比，这最后一个结果是基于MV-代数所做的工作。
In this paper we make an algebraic study of the variety of MV*-algebras introduced by C. C. Chang as an algebraic counterpart for a logic with positive and negative truth values.; We build the algebraic theory of MV*-algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in l-groups. The main results are a subdirect representation theorem, a completeness theorem, a study of simple and semisimple algebras, and a characterization of the ideal of infinitesimals as an l-group. In the last section we develop a detailed proof a the one-dimensional theorem of McNaughton, that is, the free MV*-algebra in one generator is the algebra of McNaughton functions over [−1,1]. In contrast with the rest of the paper, this last result is based on work done for MV-algebras.