Generalized MV-algebras

JOURNAL OF ALGEBRA

卷:283

Article

Galatos, N ; Tsinakis, C

关键词: residuated lattice;    MV-algebra;    lattice-ordered group;    nucleus;    categorical equivalence;   

DOI  :  10.1016/j.jalgebra.2004.07.002

来源: Elsevier

【 摘 要 】

We generalize the notion of an MV-algebra in the context of residuated lattices to include noncommutative and unbounded structures. We investigate a number of their properties and prove that they can be obtained from lattice-ordered groups via a truncation construction that generalizes the Chang-Mundici Gamma functor. This correspondence extends to a categorical equivalence that generalizes the ones established by D. Mundici and A. Dvurecenskij. The decidability of the equational theory of the variety of generalized MV-algebras follows from our analysis. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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