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Abstract:

Let Γ be Mundici's functor from the category LG whose objects are the lattice-ordered abelian groups (ℓ-groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category MV of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ℓ-group G, the Boolean skeleton of the MV-algebra Γ(G, u) is isomorphic to the Boolean algebra of factor congruences of G. © 2011 Springer Science+Business Media B.V.

Registro:

Documento: Artículo
Título:Boolean Skeletons of MV-algebras and ℓ-groups
Autor:Cignoli, R.
Filiación:Departamento de Matemtica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:ℓ-ideals; Boolean products; direct decompositions; lattice-ordered abelian groups; MV-algebras
Año:2011
Volumen:98
Número:1
Página de inicio:141
Página de fin:147
DOI: http://dx.doi.org/10.1007/s11225-011-9325-3
Título revista:Studia Logica
Título revista abreviado:Stud. Logica
ISSN:00393215
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v98_n1_p141_Cignoli

Referencias:

  • Bigard, A., Keimel, K., Wolfenstein, S., (1977) Groupes et anneaux rèticulès, Lectures Notes in Mathematics, 108. , Springer-Verlag, New York - Heildelberg - Berlin
  • Borkowski, L., (1970) Selected Works of J. Łukasiewicz, , Amsterdam: North-Holland
  • Chang, C.C., Algebraic analysis of many-valued logics (1958) Trans. Amer. Math. Soc, 88, pp. 467-490
  • Chang, C.C., A new proof of the completeness of the łukasiewicz axioms (1959) Trans. Amer. Math. Soc, 93, pp. 74-90
  • Cignoli, R., Mundici, D., An elementary proof of Chang's completeness theorem for the infinite-valued calculus of łukasiewicz (1997) Studia Logica, 58, pp. 79-97
  • Cignoli, R., Mundici, D., An invitation to Chang's MV-algebras (1997) Conference on Algebra and Model Theory, pp. 171-197. , In M. Droste and R. Göbel (eds.), Dresden 1995, Gordon and Breach, Amsterdam
  • Cignoli, R., Mundici, D., An elementary presentation of the equivalence between MV-algebras and ℓ-groups (1998) Studia Logica,, 61, pp. 49-64
  • Cignoli, R., D'Ottaviano, I.M.L., Mundici, D., (2000) Algebraic Foundations of Manyvalued Reasoning, , Dordrecht: Kluwer Academic Pub
  • Łukasiewicz, J., Tarski, A., (1930) Untersuchungen über den Aussagenkalkül, 23, pp. 30-50. , Comptes rendus de la Société des Sciences et des Lettres de Varsovie, (English translation in [2] and [11])
  • Mundici, D., Interpretation of AF C*-algebras in łukasiewicz sentential calculus (1986) J. Funct. Anal, 65, pp. 15-63
  • Tarski, A., (1983) Logic, Semantics, Metamathematics, , Clarendon Press, Oxford, 1956. Reprinted Hackett, Indianapolis
  • Torrens, A., W-algebras which are Boolean products of members of SR[1] and CW-algebras (1987) Studia Logica, 46, pp. 263-272

Citas:

---------- APA ----------
(2011) . Boolean Skeletons of MV-algebras and ℓ-groups. Studia Logica, 98(1), 141-147.
http://dx.doi.org/10.1007/s11225-011-9325-3
---------- CHICAGO ----------
Cignoli, R. "Boolean Skeletons of MV-algebras and ℓ-groups" . Studia Logica 98, no. 1 (2011) : 141-147.
http://dx.doi.org/10.1007/s11225-011-9325-3
---------- MLA ----------
Cignoli, R. "Boolean Skeletons of MV-algebras and ℓ-groups" . Studia Logica, vol. 98, no. 1, 2011, pp. 141-147.
http://dx.doi.org/10.1007/s11225-011-9325-3
---------- VANCOUVER ----------
Cignoli, R. Boolean Skeletons of MV-algebras and ℓ-groups. Stud. Logica. 2011;98(1):141-147.
http://dx.doi.org/10.1007/s11225-011-9325-3