Title:
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Subdirectly irreducible MV-algebras (English) |
Author:
|
Gaitán, Hernando |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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53 |
Issue:
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3 |
Year:
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2003 |
Pages:
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631-639 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety. (English) |
MSC:
|
03G20 |
MSC:
|
03G25 |
MSC:
|
06D25 |
MSC:
|
06D30 |
MSC:
|
06D35 |
MSC:
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06F15 |
MSC:
|
06F35 |
idZBL:
|
Zbl 1080.06013 |
idMR:
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MR2000059 |
. |
Date available:
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2009-09-24T11:05:17Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/127829 |
. |
Reference:
|
[1] W. J. Blok and D. Pigozzi: On the congruence extension property.Algebra Universalis 38 (1997), 391–394. MR 1626343, 10.1007/s000120050060 |
Reference:
|
[2] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra.Springer-Verlag, New York, 1981. MR 0648287 |
Reference:
|
[3] J. Czelakowski and W. Dziobiak: The parametrized local deduction theorem for quasivarieties of algebras and its applications.Algebra Universalis 35 (1996), 713–419. MR 1387912, 10.1007/BF01197181 |
Reference:
|
[4] C. C. Chang: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl 0084.00704, MR 0094302, 10.1090/S0002-9947-1958-0094302-9 |
Reference:
|
[5] R. Cignoli, I. M. L. D’Ottaviano and D. Mundici: Algebras of Łukasiewicz Logics, Second Edition. Editions CLE.State University of Campinas, Campinas, S. P. Brazil, 1995. |
Reference:
|
[6] A. Dinola and A. Lettieri: Equational characterization of all varieties of MV-algebras.J. Algebra 221 (1999), 463–474. MR 1726709, 10.1006/jabr.1999.7900 |
Reference:
|
[7] A. Dinola, R. Grigolia and G. Panti: Finitely generated free MV-algebras and their automorphism groups.Studia Logica 61 (1998), 65–78. MR 1639698, 10.1023/A:1005030314538 |
Reference:
|
[8] M. Font, A. J. Rogriguez and A. Torrens: Wajsberg algebras.Stochastica (1984), 5–31. MR 0780136 |
Reference:
|
[9] L. Fuchs: Partially Ordered Algebraic Systems.Pergamon Press, Oxford, 1963. Zbl 0137.02001, MR 0171864 |
Reference:
|
[10] H. Gaitán: Quasivarieties of Wajsberg algebras.J. Non-Classical Logic 8 (1991), 79–101. MR 1209377 |
Reference:
|
[11] H. Gaitán: The number simple of bounded commoutative BCK-chains with one generator.Math. Japon. 38 (1993), 483–486. MR 1221017 |
Reference:
|
[12] D. Mundici: A Short Introduction to the Algebras of Many-Valued Logic.Monograph. |
Reference:
|
[13] D. Mundici: MV-algebras are categorically equivalent to bounded commutative BCK-algebras.Math. Japon. 31 (1986), 889–894. Zbl 0633.03066, MR 0870978 |
Reference:
|
[14] A. Romanowska: Commutative BCK-chains with one generator.Math. Japon. 30 (1985), 663–670. Zbl 0583.03051, MR 0812017 |
Reference:
|
[15] A. Romanowska and T. Traczyk: On the structure of commutative BCK-chains.Math. Japon. 26 (1981), 433–442. MR 0634919 |
Reference:
|
[16] A. Romanowska and T. Traczyk: Commutative BCK-algebras. Subdirectly irreducible algebras and varieties.Math. Japon. 27 (1982), 35–48. MR 0649018 |
Reference:
|
[17] T. Traczyk: Free bounded commutative BCK-algebras with one free generator.Demonstratio Mathemetica XVI (1983), 1049–1056. MR 0744781 |
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