On semidirect and two-sided semidirect products of finite trivial monoids
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1996)
- Volume: 30, Issue: 5, page 457-482
- ISSN: 0988-3754
Access Full Article
topHow to cite
topBlanchet-Sadri, F.. "On semidirect and two-sided semidirect products of finite $\mathcal {J}$trivial monoids." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 30.5 (1996): 457-482. <http://eudml.org/doc/92546>.
@article{Blanchet1996,
author = {Blanchet-Sadri, F.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {semidirect products; locally finite pseudovarieties; finite semilattice monoids; finite aperiodic monoids; pseudovarieties of monoids},
language = {eng},
number = {5},
pages = {457-482},
publisher = {EDP-Sciences},
title = {On semidirect and two-sided semidirect products of finite $\mathcal \{J\}$trivial monoids},
url = {http://eudml.org/doc/92546},
volume = {30},
year = {1996},
}
TY - JOUR
AU - Blanchet-Sadri, F.
TI - On semidirect and two-sided semidirect products of finite $\mathcal {J}$trivial monoids
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1996
PB - EDP-Sciences
VL - 30
IS - 5
SP - 457
EP - 482
LA - eng
KW - semidirect products; locally finite pseudovarieties; finite semilattice monoids; finite aperiodic monoids; pseudovarieties of monoids
UR - http://eudml.org/doc/92546
ER -
References
top- 1. D. ALBERT, R. BALDINGER and J. RHODES, Undecidability of the identity problem for finite semigroups, Journal of Symbolic Logic, 1992, 57, pp. 179-192. Zbl0780.20035MR1150933
- 2. J. ALMEIDA, Semidirect products of pseudovarieties from the univers al algebraist's point of view, Journal of Pure and Applied Algebra, 1989, 60, pp. 113-128. Zbl0687.20053MR1020712
- 3. J. ALMEIDA, On iterated semidirect products of finite semilattices, Journal of Algebra, 1991, 142, pp. 239-254. Zbl0743.20056MR1125216
- 4. J. ALMEIDA, Semigrupos Finitos e Álgebra Universal (Institute of Mathematics and Statistics of the University of São Paulo, 1992;
- Finite Semigroups and Universal Algebra (World Scientifîc, Singapore, 1994. Zbl0844.20039MR1331143
- 5. J. ALMEIDA and P. WEIL, Free profinite semigroups over semidirect products, Izvestiya Vysshikh Učebnykh Zavedeniĭ Matematica, 1995, 1, pp. 3-31 Zbl0847.20055MR1391317
- 6. F. BLANCHET-SADRI, Some logical characterizations of the dot-depth hierarchy and applications, Ph. D. Thesis, McGill University, 1989. Zbl0831.68066MR2685431
- 7. F. BLANCHET-SADRI, Games, equations and the dot-depth hierarchy, Computers and Mathematics with Applications, 1989, 18, pp. 809-822. Zbl0682.03015MR1008808
- 8. F. BLANCHET-SADRI, On dot-depth two, RAIRO Informatique Théorique et Applications, 1990, 24, pp. 521-529. Zbl0718.68046MR1082913
- 9. F. BLANCHET-SADRI, Games, equations and dot-depth two monoids, Discrete Applied Mathematics, 1992, 39, pp.99-111. Zbl0791.20068MR1184681
- 10. F. BLANCHET-SADRI, The dot-depth of a generating class of aperiodic monoids is computable, International Journal of Foundations of Computer Science, 1992, 3, pp. 419-442. Zbl0776.68087MR1209555
- 11. BLANCHET-SADRI, Equations and dot-depth one, Semigroup Forum, 1993, 47, pp. 305-317. Zbl0814.20048MR1235764
- 12. F. BLANCHET-SADRI, Equations and monoid varieties of dot-depth one and two, Theoretïcal Computer Science, 1994, 123, pp. 239-258. Zbl0801.68105MR1256200
- 13. F. BLANCHET-SADRI, On a complete set of generators for dot-depth two, Discrete Applied Mathematics, 1994, 50, pp. 1-25. Zbl0793.68087MR1272549
- 14. F. BLANCHET-SADRI, Equations on the semidirect product of a finite semilattice by a J-trivial monoid of height k, RAIRO Informatique Théorique et Applications, 1995, 29, pp. 157-170. Zbl0833.68073MR1347591
- 15. F. BLANCHET-SADRI, Some logical characterizations of the dot-depth hierarchy and applications, Journal of Computer and System Sciences, 1995, 51, pp. 324-337. Zbl0831.68066MR1356511
- 16. F. BLANCHET-SADRI, Inclusion relations between some congraences related to the dot-depth hierarchy, Discrete Applied Mathematics, 1996, 68, pp. 33-71. Zbl0854.68051MR1393309
- 17. F. BLANCHET-SADRI and X. H. ZHANG, Equations on the semidirect product of a finite semilattice by a finite commutative monoid, Semigroup Forum, 1994, 49, pp. 67-81. Zbl0816.20052MR1272864
- 18. J. A. BRZOZOWSKI and F. E. FICH, Languages of R-trivial monoids, Journal of Computer and System Sciences, 1980, 20, pp. 32-49. Zbl0446.68066MR566640
- 19. J. A. BRZOZOWSKI and R. KNAST, The dot-depth hierarchy of star-f ree languages is infinite, Journal of Computer and System Sciences, 1978, 16, pp. 37-55. Zbl0368.68074MR471451
- 20. S. BURRIS and H. P. SANKAPPANAVAR, A Course in Universal Algebra, Springer-Verlag, New York, 1981. Zbl0478.08001MR648287
- 21. R. S. COHEN and J. A. BRZOZOWSKI, Dot-depth of star-free events, Journal of Computer and System Sciences, 1971, 5, pp. 1-15. Zbl0217.29602MR309676
- 22. A. EHRENFEUCHT, An application of games to the completeness problems for formalized theories, Fundamenta Mathematicae, 1961, 49, pp. 129-141. Zbl0096.24303MR126370
- 23. S. EILENBERG, Automata, Languages, and Machines, Vol. A, Academie Press, New York, 1974; Vol. B, Academic Press, New York, 1976. Zbl0359.94067MR530382
- 24. S. EILENBERG and M. P. SCHÜTZENBERGER, On pseudovarieties, Advances in Mathematics, 1976, 79, pp. 413-418. Zbl0351.20035MR401604
- 25. C. IRASTORZA, Base non finie de variétés, in STACS'85, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1985, 182, pp. 180-186. Zbl0572.20041MR786881
- 26. D. PERRIN and J. E PIN, First order logic andstar-free sets, Journal of Computer and System Sciences, 1986, 32, pp. 393-406. Zbl0618.03015MR858236
- 27. J. E. PIN, Variétés de Langages Formels, Masson, Paris, 1984; Varieties of Formal Languages, North Oxford Academic, London, 1986 and Plenum, NewYork, 1986. Zbl0636.68093MR752695
- 28. J. E. PIN, Hiérarchies de concaténation, RAIRO Informatique Théorique et Applications, 1984, 18, pp.23-46. Zbl0559.68062MR750449
- 29. J. E. PIN, On semidirect products of two finite semilattices, Semigroup Forum, 1984, 28, pp.73-81. Zbl0527.20046MR729653
- 30. J. REITERMAN, The Birkhoff theorem for varieties of finite algebras, Algebra Universalis, 1982, 14, pp. 1-10. Zbl0484.08007MR634411
- 31. J. RHODES and B. TILSON, The kernel of monoid morphisms, Journal of Pure and Applied Algebra, 1989, 62, pp. 227-268. Zbl0698.20056MR1026876
- 32. I. SIMON, Hierarchies of events of dot-depth one, Ph. D. Thesis, University of Waterloo, 1972. MR2623305
- 33. I. SIMON, Piecewise testable events in Proc. 2nd GI Conf., Lecture Notes in Computer Science, 1975, 33, Springer-Verlag, Berlin, pp. 214-222. Zbl0316.68034MR427498
- 34. P. STIFFLER, Extension of the fundamental theorem of finite semigroups, Advances in Mathematics, 1973, 77, pp. 159-209.
- 35. H. STRAUBING, Finite semigroup varieties of the form V * D, Journal of Pure and Applied Algebra, 1985, 36, pp. 53-94. Zbl0561.20042MR782639
- 36. H. STRAUBING and P. WEIL, On a conjecture concerning dot-depth two languages, Theoretical Computer Science, 1992, 104, pp. 161-183. Zbl0762.68037MR1186177
- 37. W. THOMAS, Classifying regular events in symbolic logic, Journal of Computer and System Sciences, 1982, 25, pp. 360-376. Zbl0503.68055MR684265
- 38. W. THOMAS, An application of the Ehrenfeucht-Fraïssé game in formal language theory, Mémoires de la Société Mathématique de France, 1984, 16, pp. 11-21. Zbl0558.68064MR792490
- 39. B. TILSON, Categories as algebra: an essential ingredient in the theory of semigroups, Journal of Pure andApplied Algebra, 1987, 48, pp. 83-198. Zbl0627.20031MR915990
- 40. P. WEIL, Closure of varieties of languages under products with counter, Journal of Computer and System Sciences, 1992, 45, pp. 316-339. Zbl0766.20023MR1193376
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.