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Abstract:

The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to σ-complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for these algebras are given. These results are applied to obtain versions of the Cantor-Bernstein-Schröder theorem for σ-complete orthomodular lattices, Stone algebras, BL-algebras, MV-algebras, pseudo MV-algebras, Łukasiewicz and Post algebras of order n.

Registro:

Documento: Artículo
Título:An algebraic version of the Cantor-Bernstein-Schröder theorem
Autor:Freytes, H.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas Y Naturales, Univ. Buenos Aires, Cd. U., Argentina
Palabras clave:central elements; factor congruences; lattices; varieties
Año:2004
Volumen:54
Número:3
Página de inicio:609
Página de fin:621
DOI: http://dx.doi.org/10.1007/s10587-004-6412-x
Título revista:Czechoslovak Mathematical Journal
Título revista abreviado:Czech. Math. J.
ISSN:00114642
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00114642_v54_n3_p609_Freytes

Referencias:

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Citas:

---------- APA ----------
(2004) . An algebraic version of the Cantor-Bernstein-Schröder theorem. Czechoslovak Mathematical Journal, 54(3), 609-621.
http://dx.doi.org/10.1007/s10587-004-6412-x
---------- CHICAGO ----------
Freytes, H. "An algebraic version of the Cantor-Bernstein-Schröder theorem" . Czechoslovak Mathematical Journal 54, no. 3 (2004) : 609-621.
http://dx.doi.org/10.1007/s10587-004-6412-x
---------- MLA ----------
Freytes, H. "An algebraic version of the Cantor-Bernstein-Schröder theorem" . Czechoslovak Mathematical Journal, vol. 54, no. 3, 2004, pp. 609-621.
http://dx.doi.org/10.1007/s10587-004-6412-x
---------- VANCOUVER ----------
Freytes, H. An algebraic version of the Cantor-Bernstein-Schröder theorem. Czech. Math. J. 2004;54(3):609-621.
http://dx.doi.org/10.1007/s10587-004-6412-x