An algebraic version of the Cantor-Bernstein-Schröder theorem

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 structu...

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Autor principal: Freytes, H.
Formato: JOUR
Materias:
central elements
factor congruences
lattices
varieties
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00114642_v54_n3_p609_Freytes
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00114642_v54_n3_p609_Freytes
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spelling todo:paper_00114642_v54_n3_p609_Freytes2023-10-03T14:09:52Z An algebraic version of the Cantor-Bernstein-Schröder theorem Freytes, H. central elements factor congruences lattices varieties 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. Fil:Freytes, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00114642_v54_n3_p609_Freytes
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic central elements
factor congruences
lattices
varieties
spellingShingle central elements
factor congruences
lattices
varieties
Freytes, H.
An algebraic version of the Cantor-Bernstein-Schröder theorem
topic_facet central elements
factor congruences
lattices
varieties
description 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.
format JOUR
author Freytes, H.
author_facet Freytes, H.
author_sort Freytes, H.
title An algebraic version of the Cantor-Bernstein-Schröder theorem
title_short An algebraic version of the Cantor-Bernstein-Schröder theorem
title_full An algebraic version of the Cantor-Bernstein-Schröder theorem
title_fullStr An algebraic version of the Cantor-Bernstein-Schröder theorem
title_full_unstemmed An algebraic version of the Cantor-Bernstein-Schröder theorem
title_sort algebraic version of the cantor-bernstein-schröder theorem
url http://hdl.handle.net/20.500.12110/paper_00114642_v54_n3_p609_Freytes
work_keys_str_mv AT freytesh analgebraicversionofthecantorbernsteinschrodertheorem
AT freytesh algebraicversionofthecantorbernsteinschrodertheorem
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