| Title:
|
On a theorem of Cantor-Bernstein type for algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
1-14 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices. (English) |
| Keyword:
|
lattice |
| Keyword:
|
$\mathcal L^*$-variety |
| Keyword:
|
center |
| Keyword:
|
internal direct factor |
| MSC:
|
06B99 |
| idZBL:
|
Zbl 1174.06308 |
| idMR:
|
MR2402522 |
| . |
| Date available:
|
2009-09-24T11:53:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128242 |
| . |
| Reference:
|
[1] R. Cignoli, I. D. D’Ottaviano, and D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[2] A. De Simone, D. Mundici, and M. Navara: A Cantor-Bernstein theorem for $\sigma $-complete $MV$-algebras.Czechoslovak Math. J. 53 (2003), 437–447. MR 1983464, 10.1023/A:1026299723322 |
| Reference:
|
[3] A. De Simone, M. Navara, and P. Pták: On interval homogeneous orthomodular lattices.Commentat. Math. Univ. Carolinae 42 (2001), 23–30. MR 1825370 |
| Reference:
|
[4] A. Dvurečenskij: Central elements and Cantor-Bernstein’s theorem for pseudo-effect algebras.J. Aust. Math. Soc. 74 (2003), 121–143. MR 1948263, 10.1017/S1446788700003177 |
| Reference:
|
[5] H. Freytes: An algebraic version of the Cantor-Bernstein-Schröder theorem.Czechoslovak Math. J. 54 (2004), 609–621. Zbl 1080.06008, MR 2086720, 10.1007/s10587-004-6412-x |
| Reference:
|
[6] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.Proc. Fourth Int. Symp. Econ. Informatics, Bucharest, 1999, pp. 961–968. MR 1730100 |
| Reference:
|
[7] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras.Multiple-valued Logics 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[8] J. Hashimoto: On the product decomposition of partially ordered sets.Math. Jap. 1 (1948), 120–123. Zbl 0041.37801, MR 0030502 |
| Reference:
|
[9] J. Jakubík: Direct product decompositions of partially ordered groups.Czechoslovak Math. J. 10 (1960), 231–243. (Russian) |
| Reference:
|
[10] J. Jakubík: Cantor-Bernstein theorem for lattice ordered groups.Czechoslovak Math. J. 22 (1972), 159-175. MR 0297666 |
| Reference:
|
[11] J. Jakubík, M. Csontóová: Convex isomorphisms of directed multilattices.Math. Bohem. 118 (1993), 359–378. MR 1251882 |
| Reference:
|
[12] J. Jakubík: Complete lattice ordered groups with strong units.Czechoslovak Math. J. 46 (1996), 221–230. MR 1388611 |
| Reference:
|
[13] J. Jakubík: Convex isomorphisms of archimedean lattice ordered groups.Mathware and Soft Computing 5 (1998), 49–56. MR 1632739 |
| Reference:
|
[14] J. Jakubík: Cantor-Bernstein theorem for $MV$-algebras.Czechoslovak Math. J. 49 (1999), 517–526. MR 1708370, 10.1023/A:1022467218309 |
| Reference:
|
[15] J. Jakubík: Direct product decompositions of infinitely distributive lattices.Math. Bohemica 125 (2000), 341–354. MR 1790125 |
| Reference:
|
[16] J. Jakubík: Convex mappings of archimedean $MV$-algebras.Math. Slovaca 51 (2001), 383–391. MR 1864107 |
| Reference:
|
[17] J. Jakubík: Direct product decompositions of pseudo $MV$-algebras.Arch. Math. 37 (2002), 131–142. MR 1838410 |
| Reference:
|
[18] J. Jakubík: Cantor-Bernstein theorem for lattices.Math. Bohem. 127 (2002), 463–471. MR 1931330 |
| Reference:
|
[19] J. Jakubík: A theorem of Cantor-Bernstein type for orthogonally $\sigma $-complete pseudo $MV$-algebras.Tatra Mt. Math. Publ. 22 (2002), 91–103. MR 1889037 |
| Reference:
|
[20] G. Jenča: A Cantor-Bernstein type theorem for effect algebras.Algebra Univers. 48 (2002), 399–411. MR 1967089 |
| Reference:
|
[21] A. G. Kurosh: Group Theory.Nauka, Moskva, 1953. (Russian) |
| Reference:
|
[22] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52 (2002), 255–273. MR 1905434, 10.1023/A:1021766309509 |
| Reference:
|
[23] R. Sikorski: A generalization of theorem of Banach and Cantor-Bernstein.Colloq. Math. 1 (1948), 140–144. MR 0027264, 10.4064/cm-1-2-140-144 |
| Reference:
|
[24] A. Tarski: Cardinal Algebras.Oxford University Press, New York, 1949. Zbl 0041.34502, MR 0029954 |
| . |
