MV-代数与部分循环序群
Mv-algebras And Partially Cyclically Ordered Groups
摘要：
证明了MV-代数与缠绕在格-序群上的部分循环序群之间存在函子对应。由此，循环序群的一些结果可以用MV-代数来表述。例如，研究群与循环序可以得到一阶的幺模复数群和有限循环群群的特征。我们推导出伪有限MV-链和伪简单MV-链（即共享相同的一阶属性作为一些简单的）的一个特征。这些结果可以推广到一些非线性序MV-代数，例如超阿基米德MV-代数。
英文摘要：
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated in terms of MV-algebras. For example, the study of groups together with a cyclic order allows to get a first-order characterization of groups of unimodular complex numbers and of finite cyclic groups. We deduce a characterization of pseudofinite MV-chains and of pseudo-simple MV-chains (i.e. which share the same first-order properties as some simple ones). We can generalize these results to some non-lineraly ordered MV-algebras, for example hyper-archimedean MV-algebras.
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