On semidirect and two-sided semidirect products of finite 𝒥trivial monoids
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 5, pp. 457-482.
@article{ITA_1996__30_5_457_0,
     author = {Blanchet-Sadri, F.},
     title = {On semidirect and two-sided semidirect products of finite $\mathcal {J}$trivial monoids},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {457--482},
     publisher = {EDP-Sciences},
     volume = {30},
     number = {5},
     year = {1996},
     zbl = {0906.20039},
     mrnumber = {1435733},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1996__30_5_457_0/}
}
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
DA  - 1996///
SP  - 457
EP  - 482
VL  - 30
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_1996__30_5_457_0/
UR  - https://zbmath.org/?q=an%3A0906.20039
UR  - https://www.ams.org/mathscinet-getitem?mr=1435733
LA  - en
ID  - ITA_1996__30_5_457_0
ER  - 
Blanchet-Sadri, F. On semidirect and two-sided semidirect products of finite $\mathcal {J}$trivial monoids. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 5, pp. 457-482. http://www.numdam.org/item/ITA_1996__30_5_457_0/

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. | MR 1150933 | Zbl 0780.20035

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. | MR 1020712 | Zbl 0687.20053

3. J. Almeida, On iterated semidirect products of finite semilattices, Journal of Algebra, 1991, 142, pp. 239-254. | MR 1125216 | Zbl 0743.20056

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. | MR 1331143 | Zbl 0844.20039

5. J. Almeida and P. Weil, Free profinite semigroups over semidirect products, Izvestiya Vysshikh Učebnykh Zavedeniĭ Matematica, 1995, 1, pp. 3-31 | MR 1391317 | Zbl 0847.20055

6. F. Blanchet-Sadri, Some logical characterizations of the dot-depth hierarchy and applications, Ph. D. Thesis, McGill University, 1989. | MR 2685431

7. F. Blanchet-Sadri, Games, equations and the dot-depth hierarchy, Computers and Mathematics with Applications, 1989, 18, pp. 809-822. | MR 1008808 | Zbl 0682.03015

8. F. Blanchet-Sadri, On dot-depth two, RAIRO Informatique Théorique et Applications, 1990, 24, pp. 521-529. | Numdam | MR 1082913 | Zbl 0718.68046

9. F. Blanchet-Sadri, Games, equations and dot-depth two monoids, Discrete Applied Mathematics, 1992, 39, pp.99-111. | MR 1184681 | Zbl 0791.20068

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. | MR 1209555 | Zbl 0776.68087

11. Blanchet-Sadri, Equations and dot-depth one, Semigroup Forum, 1993, 47, pp. 305-317. | MR 1235764 | Zbl 0814.20048

12. F. Blanchet-Sadri, Equations and monoid varieties of dot-depth one and two, Theoretïcal Computer Science, 1994, 123, pp. 239-258. | MR 1256200 | Zbl 0801.68105

13. F. Blanchet-Sadri, On a complete set of generators for dot-depth two, Discrete Applied Mathematics, 1994, 50, pp. 1-25. | MR 1272549 | Zbl 0793.68087

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. | Numdam | MR 1347591 | Zbl 0833.68073

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. | MR 1356511 | Zbl 0831.68066

16. F. Blanchet-Sadri, Inclusion relations between some congraences related to the dot-depth hierarchy, Discrete Applied Mathematics, 1996, 68, pp. 33-71. | MR 1393309 | Zbl 0854.68051

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. | MR 1272864 | Zbl 0816.20052

18. J. A. Brzozowski and F. E. Fich, Languages of R-trivial monoids, Journal of Computer and System Sciences, 1980, 20, pp. 32-49. | MR 566640 | Zbl 0446.68066

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. | MR 471451 | Zbl 0368.68074

20. S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York, 1981. | MR 648287 | Zbl 0478.08001

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. | MR 309676 | Zbl 0217.29602

22. A. Ehrenfeucht, An application of games to the completeness problems for formalized theories, Fundamenta Mathematicae, 1961, 49, pp. 129-141. | MR 126370 | Zbl 0096.24303

23. S. Eilenberg, Automata, Languages, and Machines, Vol. A, Academie Press, New York, 1974; Vol. B, Academic Press, New York, 1976. | MR 530382 | Zbl 0359.94067

24. S. Eilenberg and M. P. Schützenberger, On pseudovarieties, Advances in Mathematics, 1976, 79, pp. 413-418. | MR 401604 | Zbl 0351.20035

25. C. Irastorza, Base non finie de variétés, in STACS'85, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1985, 182, pp. 180-186. | MR 786881 | Zbl 0572.20041

26. D. Perrin and J. E Pin, First order logic andstar-free sets, Journal of Computer and System Sciences, 1986, 32, pp. 393-406. | MR 858236 | Zbl 0618.03015

27. J. E. Pin, Variétés de Langages Formels, Masson, Paris, 1984; Varieties of Formal Languages, North Oxford Academic, London, 1986 and Plenum, NewYork, 1986. | MR 752695 | Zbl 0636.68093

28. J. E. Pin, Hiérarchies de concaténation, RAIRO Informatique Théorique et Applications, 1984, 18, pp.23-46. | Numdam | MR 750449 | Zbl 0559.68062

29. J. E. Pin, On semidirect products of two finite semilattices, Semigroup Forum, 1984, 28, pp.73-81. | MR 729653 | Zbl 0527.20046

30. J. Reiterman, The Birkhoff theorem for varieties of finite algebras, Algebra Universalis, 1982, 14, pp. 1-10. | MR 634411 | Zbl 0484.08007

31. J. Rhodes and B. Tilson, The kernel of monoid morphisms, Journal of Pure and Applied Algebra, 1989, 62, pp. 227-268. | MR 1026876 | Zbl 0698.20056

32. I. Simon, Hierarchies of events of dot-depth one, Ph. D. Thesis, University of Waterloo, 1972. | MR 2623305

33. I. Simon, Piecewise testable events in Proc. 2nd GI Conf., Lecture Notes in Computer Science, 1975, 33, Springer-Verlag, Berlin, pp. 214-222. | MR 427498 | Zbl 0316.68034

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. | MR 782639 | Zbl 0561.20042

36. H. Straubing and P. Weil, On a conjecture concerning dot-depth two languages, Theoretical Computer Science, 1992, 104, pp. 161-183. | MR 1186177 | Zbl 0762.68037

37. W. Thomas, Classifying regular events in symbolic logic, Journal of Computer and System Sciences, 1982, 25, pp. 360-376. | MR 684265 | Zbl 0503.68055

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. | Numdam | MR 792490 | Zbl 0558.68064

39. B. Tilson, Categories as algebra: an essential ingredient in the theory of semigroups, Journal of Pure andApplied Algebra, 1987, 48, pp. 83-198. | MR 915990 | Zbl 0627.20031

40. P. Weil, Closure of varieties of languages under products with counter, Journal of Computer and System Sciences, 1992, 45, pp. 316-339. | MR 1193376 | Zbl 0766.20023