| 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:
|
http://hdl.handle.net/10338.dmlcz/128190 |
| . |
| 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 |
| . |
