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Title: Subdirect products of certain varieties of unary algebras (English)
Author: Ćirić, M.
Author: Petković, T.
Author: Bogdanović, S.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 57
Issue: 2
Year: 2007
Pages: 573-578
Summary lang: English
Category: math
Summary: J. Płonka in [12] noted that one could expect that the regularization ${\mathcal R}(K)$ of a variety ${K}$ of unary algebras is a subdirect product of ${K}$ and the variety ${D}$ of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties ${K}$ which are contained in the generalized variety ${TDir}$ of the so-called trap-directable algebras. (English)
Keyword: unary algebra
Keyword: subdirect product
Keyword: variety
Keyword: directable algebra
MSC: 08A60
MSC: 08A70
MSC: 08B15
MSC: 08B26
idZBL: Zbl 1174.08301
idMR: MR2337615
Date available: 2009-09-24T11:47:39Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] C. J.  Ash: Pseudovarieties, generalized varieties and similarly described classes.J. Algebra 92 (1985), 104–115. Zbl 0548.08007, MR 0772473
Reference: [2] S.  Bogdanović, M.  Ćirić, B.  Imreh, T.  Petković, and M.  Steinby: On local properties of unary algebras.Algebra Colloquium 10 (2003), 461–478. MR 2013740
Reference: [3] S.  Bogdanović, M.  Ćirić, and T.  Petković: Generalized varieties of algebras.Internat. J.  Algebra Comput, Submitted.
Reference: [4] S.  Bogdanović, M.  Ćirić,  T. Petković, B.  Imreh, and M.  Steinby: Traps, cores, extensions and subdirect decompositions of unary algebras.Fundamenta Informaticae 34 (1999), 51–60. MR 1718110, 10.3233/FI-1999-381205
Reference: [5] S.  Bogdanović, B.  Imreh, M.  Ćirić, and T.  Petković: Directable automata and their generalizations. A survey.Novi Sad J.  Math. 29 (1999), 31–74. MR 1818327
Reference: [6] S.  Burris, H. P.  Sankappanavar: A Course in Universal Algebra.Springer-Verlag, New York, 1981. MR 0648287
Reference: [7] M.  Ćirić, S.  Bogdanović: Lattices of subautomata and direct sum decompositions of automata.Algebra Colloquium 6 (1999), 71–88. MR 1680653
Reference: [8] F.  Gécseg, I.  Peák: Algebraic Theory of Automata.Akadémiai Kiadó, Budapest, 1971. MR 0332374
Reference: [9] G.  Grätzer: Universal Algebra, 2nd ed.Springer-Verlag, New York-Heidelberg-Berlin, 1979. MR 0538623
Reference: [10] T.  Petković, M.  Ćirić, and S.  Bogdanović: Decompositions of automata and transition semigroups.Acta Cybernetica (Szeged) 13 (1998), 385–403. MR 1681152
Reference: [11] J.  Płonka: On the sum of a system of disjoint unary algebras corresponding to a given type.Bull. Acad. Pol. Sci., Ser. Sci. Math. 30 (1982), 305–309. MR 0707740
Reference: [12] J. Płonka: On the lattice of varieties of unary algebras.Simon Stevin 59 (1985), 353–364. MR 0840857


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