Title:
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Abelian differential modes are quasi-affine (English) |
Author:
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Stanovský, David |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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53 |
Issue:
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3 |
Year:
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2012 |
Pages:
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461-473 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings. (English) |
Keyword:
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differential modes |
Keyword:
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abelian algebras |
Keyword:
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quasi-affine algebras |
Keyword:
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subreducts of modules |
MSC:
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08A05 |
MSC:
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15A78 |
idZBL:
|
Zbl 1265.08002 |
idMR:
|
MR3017843 |
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Date available:
|
2012-08-31T11:43:48Z |
Last updated:
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2014-10-06 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/142937 |
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Reference:
|
[1] Gumm H.P.: Algebras in permutable varieties: geometrical properties of affine algebras.Algebra Universalis 9 (1979), no. 1, 8–34. Zbl 0414.08002, MR 0508666, 10.1007/BF02488013 |
Reference:
|
[2] Kearnes K.: The structure of finite modes.manuscript, 1990's. |
Reference:
|
[3] Kearnes K.: Subdirectly irreducible modes.Discuss. Math. Algebra Stochastic Methods 19 (1999), no. 1, 129–145. Zbl 0948.08001, MR 1709965 |
Reference:
|
[4] Kearnes K., Szendrei Á.: The relationship between two commutators.Internat. J. Algebra Comput. 8 (1998), no. 4, 497–531. Zbl 0923.08001, MR 1663558, 10.1142/S0218196798000247 |
Reference:
|
[5] Kravchenko A., Pilitowska A., Romanowska A., Stanovský D.: Differential modes.Internat. J. Algebra Comput. 18 (2008), no. 3, 567–588. Zbl 1144.08001, MR 2422073, 10.1142/S0218196708004561 |
Reference:
|
[6] Padmanabhan R., Penner P.: An implication basis for linear forms.Algebra Universalis 55 (2006), no. 2–3, 355–368. Zbl 1108.08006, MR 2280237, 10.1007/s00012-006-1994-9 |
Reference:
|
[7] Pilitowska A., Romanowska A., Stanovský D.: Varieties of differential modes embeddable into semimodules.Internat. J. Algebra Comput. 19 (2009), no. 5, 669–680. Zbl 1173.08002, MR 2547063, 10.1142/S0218196709005305 |
Reference:
|
[8] Quackenbush R.: Quasi-affine algebras.Algebra Universalis 20 (1985), 318–327. Zbl 0573.08003, MR 0811692, 10.1007/BF01195141 |
Reference:
|
[9] Romanowska A.: Semi-affine modes and modals.Sci. Math. Jpn. 61 (2005), 159–194. Zbl 1067.08001, MR 2111551 |
Reference:
|
[10] Romanowska A.B., Smith J.D.H.: Differential groupoids.Contributions to General Algebra 7 (1991), 283–290. Zbl 0744.20055, MR 1143092 |
Reference:
|
[11] Romanowska A., Smith J.D.H.: Modes.World Scientific, River Edge, NJ, 2002. Zbl 1060.08009, MR 1932199 |
Reference:
|
[12] Smith J.D.H.: Mal'cev varieties.Lecture Notes in Mathematics, 554, Springer, Berlin, 1976. Zbl 0344.08002, MR 0432511 |
Reference:
|
[13] Stanovský D.: Idempotent subreducts of semimodules over commutative semirings.Rend. Semin. Mat. Univ. Padova 121 (2009), 33–43. Zbl 1190.16054, MR 2542133, 10.4171/RSMUP/121-3 |
Reference:
|
[14] Stanovský D.: Subdirectly irreducible differential modes.Internat. J. Algebra Comput.(to appear). |
Reference:
|
[15] Stronkowski M.: Embedding entropic algebras into semimodules and modules.Internat. J. Algebra Comput. 19 (2009), no. 8, 1025–1047. Zbl 1193.08001, MR 2603717, 10.1142/S0218196709005470 |
Reference:
|
[16] Stronkowski M., Stanovský D.: Embedding general algebras into modules.Proc. Amer. Math. Soc. 138 (2010), no. 8, 2687–2699. Zbl 1206.08002, MR 2644885, 10.1090/S0002-9939-10-10356-6 |
Reference:
|
[17] Szendrei Á.: Modules in general algebra.Contributions to General Algebra 10 (1998), 41–53. Zbl 0912.08001, MR 1648809 |
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