On the geometric theory of local MV-algebras

JOURNAL OF ALGEBRA

卷:479

Article

Caramello, O.¹  Russo, A. C.^2,3 

[1] Inst Hautes Etud Sci, 35 Route Chartres, F-91440 Bures Sur Yvette, France

[2] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo 2,132, I-84084 Fisciano, SA, Italy

[3] Univ Paris Diderot, 5 Rue Thomas Mann, F-75013 Paris, France

关键词: Local MV-algebra;    Lattice-ordered abelian group;    Morita-equivalence;    Geometric logic;    Classifying topos;    Grothendieck topology;    Theory of presheaf type;   

DOI  :  10.1016/j.jalgebra.2017.01.005

来源: Elsevier

【 摘 要 】

We investigate the geometric theory of local MV-algebras and its quotients axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We show that, whilst the theory of local MV-algebras is not of pre-sheaf type, each of these quotients is a theory of presheaf type which is Morita equivalent to an expansion of the theory of lattice-ordered abelian groups. Di Nola Lettieri's equivalence is recovered from the Morita-equivalence for the quotient axiomatizing the local MV-algebras in Chang's variety, that is, the perfect APT-algebras. We establish along the way a number of results of independent interest, including a constructive treatment of the radical for MV-algebras in a fixed proper variety of MV-algebras and a representation theorem for the finitely presentable algebras in such a variety as finite products of local MV-algebras. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free