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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2004
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| 100 | 1 | |a Freytes Solari, Héctor Carlos | |
| 245 | 1 | 3 | |a An algebraic version of the Cantor-Bernstein-Schröder theorem |
| 260 | |c 2004 | ||
| 270 | 1 | 0 | |m Departamento de Matemática, Fac. de Ciencias Exactas Y Naturales, Univ. Buenos Aires, Cd. U.Argentina; email: hfreytes@dm.uba.ar |
| 504 | |a Balbes, R., Dwinger, Ph., (1974) Distributive Lattices, , University of Missouri Press, Columbia | ||
| 504 | |a Birkhoff, G., (1967) Lattice Theory, Third Edition, , AMS, Providence | ||
| 504 | |a Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S., (1991) ŁUkasiewicz-Moisil Algebras, , North-Holland, Amsterdam | ||
| 504 | |a Cignoli, R., Representation of Łukasiewicz and Post algebras by continuous functions (1972) Colloq. Math., 24, pp. 127-138 | ||
| 504 | |a R. Cignoli: Lectures at Buenos Aires University. 2000; Cignoli, R., D'Ottaviano, M.I., Mundici, D., (2000) Algebraic Foundations of Many-Valued Reasoning, , Kluwer, Dordrecht | ||
| 504 | |a Cignoli, R., Torrens, A., An algebraic analysis of product logic (2000) Multiple Valued Logic, 5, pp. 45-65 | ||
| 504 | |a De Simone, A., Mundici, D., Navara, M., A Cantor-Bernstein Theorem for complete MV-algebras (2003) Czechoslovak Math. J, 53, pp. 437-447 | ||
| 504 | |a De Simone, A., Navara, M., Pták, P., On interval homogeneous orthomodular lattices (2001) Comment. Math. Univ. Carolin., 42, pp. 23-30 | ||
| 504 | |a Dvurečenskij, A., Pseudo MV-algebras are intervals in l-groups (2002) J. Austral. Math. Soc. (Ser. A), 72, pp. 427-445 | ||
| 504 | |a Dvurečenskij, A., On pseudo MV-algebras (2001) Soft Computing, 5, pp. 347-354 | ||
| 504 | |a Georgescu, G., Iorgulescu, A., Pseudo MV-algebras | ||
| 504 | |a Hájek, P., (1998) Metamathematics of Fuzzy Logic, , Kluwer, Dordrecht | ||
| 504 | |a Höhle, U., Commutative, residuated l-monoids (1995) A Handbook on the Mathematical Foundations of Fuzzy Set Theory, , Non-Classical Logics and their Applications to Fuzzy Subset. (U. Höhle, E. P. Klement, eds.). Kluwer, Dordrecht | ||
| 504 | |a Jakubík, J., A theorem of Cantor-Bernstein type for orthogonally σ-complete pseudo MV-algebras Czechoslovak Math. J., , To appear | ||
| 504 | |a Kalman, J.A., Lattices with involution (1958) Trans. Amer. Math. Soc., 87, pp. 485-491 | ||
| 504 | |a Koppelberg, S., (1989) Handbook of Boolean Algebras, 1. , (J. Donald Monk, ed.). North Holland, Amsterdam | ||
| 504 | |a Kowalski, T., Ono, H., (2000) Residuated Lattices: An Algebraic Glimpse at Logics Without Contraction, , Preliminary report | ||
| 504 | |a Maeda, F., Maeda, S., (1970) Theory of Symmetric Lattices, , Springer-Verlag, Berlin | ||
| 504 | |a Sikorski, R., A generalization of theorem of Banach and Cantor-Bernstein (1948) Colloq. Math., 1, pp. 140-144 | ||
| 504 | |a Tarski, A., (1949) Cardinal Algebras, , Oxford University Press, New York | ||
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a 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. |l eng | |
| 536 | |a Detalles de la financiación: During the preparation of this paper the author was supported by a Fellowship from the FOMEC Program. | ||
| 593 | |a Departamento de Matemática, Fac. de Ciencias Exactas Y Naturales, Univ. Buenos Aires, Cd. U., Argentina | ||
| 690 | 1 | 0 | |a CENTRAL ELEMENTS |
| 690 | 1 | 0 | |a FACTOR CONGRUENCES |
| 690 | 1 | 0 | |a LATTICES |
| 690 | 1 | 0 | |a VARIETIES |
| 773 | 0 | |d 2004 |g v. 54 |h pp. 609-621 |k n. 3 |p Czech. Math. J. |x 00114642 |t Czechoslovak Mathematical Journal | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s10587-004-6412-x |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00114642_v54_n3_p609_Freytes |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00114642_v54_n3_p609_Freytes |y Registro en la Biblioteca Digital |
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