Profinite categories and semidirect products

Journal of Pure and Applied Algebra

Volumn 123, Issue 1-3, 1998, Pages 1-50

  Almeida, J ^a   Weil, P ^b  

^a UNIVERSITY OF PORTO   (Portugal)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031608031     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(96)00083-7     Document Type: Article

References (32)

1. [1] J. Almeida, Semidirect products of pseudovarieties from the universal algebraist's point of view, J. Pure Appl. Algebra 60 (1989) 113-128.
2. [2] J. Almeida, Implicit operations on finite script J sign-trivial semigroups and a conjecture of I. Simon, J. Pure Appl. Algebra 69 (1990) 205-218.
3. [3] J. Almeida, Implicit operations and Knast's theorem, in: C. Bonzini, A. Cherubini, and C. Tibiletti, eds., Semigroups: Algebraic Theory and Applications to Formal Languages and Codes (World Scientific, Singapore, 1993) 1-16.
4. [4] J. Almeida, Finite Semigroups and Universal Algebra (World Scientific, Singapore, 1995) English translation.
5. [5] J. Almeida, A syntactical proof of locality of DA, Int. J. Algebra Comput, to appear.
6. [6] J. Almeida and A. Azevedo, On regular implicit operations, Portugaliae Math. 50 (1993) 35-61.
7. [7] J. Almeida and P. Weil, Free profinite semigroups over semidirect products, Russian Math. (Iz. VUZ) 39 (1995) 1-27.
8. [8] J. Almeida and P. Weil, Relatively free profinite monoids: an introduction and examples, in: J.B. Fountain, ed., Semigroups, Formal Languages and Groups, Vol. 466 (Kluwer, Dordrecht, 1995) 73-117.
9. [9] C.J. Ash, Finite semigroups with commuting idempotents, J. Austral. Math. Soc. Ser. A 43 (1987) 81-90.
10. [10] K. Auinger, personal communication.
11. [11] A. Azevedo, Operations preserving homomorphisms on the class of finite semigroups DS, in: J. Almeida, ed., Actas II Encontro de Algebristas Portugueses (Universidade de Porto, Porto, 1987) 33-43.
12. [12] B. Banaschewski, The Birkhoff theorem for varieties of finite algebras, Algebra Universalis 17 (1983) 360-368.
13. [13] J.A. Brzozowski and F.E. Fich, On generalized locally testable semigroups, Discrete Math. 50 (1984) 153-169.
14. [14] J.A. Brzozowski and I. Simon, Characterizations of locally testable events, Discrete Math. 4 (1973) 243-271.
15. [15] S. Eilenberg, Automata, Languages and Machines, Vol. B (Academic Press, New York, 1976).
16. [16] R.P. Hunter, Certain finitely generated compact zero-dimensional semigroups, J. Austral. Math. Soc. Ser. A 44 (1988) 265-270.
17. [17] P.R. Jones, Profinite categories, implicit operations and pseudovarieties of categories, Int. J. Algebra Comput., to appear.
18. [18] P.R. Jones and S. Pustejovsky, A kernel for relational morphisms of categories, in: J.M. Howie, W.D. Munn and H.J. Weinert, eds., Semigroups with Applications (World Scientific, Singapore, 1992) 152-161.
19. [19] R. Knast, A semigroup characterization of dot-depth one languages, RAIRO Inform. Théor. Appl. 17 (1983) 321-330.
20. [20] R. Knast, Some theorems on graph congruences, RAIRO Inform. Théor. Appl. 17 (1983) 331-342.
21. [21] S.W. Margolis, Kernels and expansions: an historical and technical perspective, in: J. Rhodes, ed., Monoids and Semigroups with Applications (World Scientific, Singapore, 1991) 3-30.
22. [22] S.W. Margolis and J.-E. Pin, Inverse semigroups and extensions of groups by semilattices, J. Algebra 110 (1987) 277-297.
23. [23] S.W. Margolis and J.-E. Pin, Inverse semigroups and varieties of finite semigroups, J. Algebra 110 (1987) 306-323.
24. [24] J.-E. Pin, On a conjecture of Rhodes, Semigroup Forum 39 (1989) 1-15.
25. [25] J. Reiterman, The Birkhoff theorem for finite algebras, Algebra Universalis 14 (1982) 1-10.
26. [26] J. Rhodes and B. Tilson, The kernel of monoid morphisms, J. Pure Appl. Algebra 62 (1989) 227-268.
27. [27] J. Rhodes and P. Weil, Decomposition techniques for finite semigroups, using categories II, J. Pure Appl. Algebra 62 (1989) 285-312.
28. [28] L. Ribes and P.A. Zalesskiǐ, The pro-p topology of a free group and algorithmic problems in semigroups, Int. J. Algebra Comput. 4 (1994) 359-374.
29. [29] H. Straubing, Finite semigroup varieties of the form V * D, J. Pure Appl. Algebra 36 (1985) 53-94.
30. [30] D. Thérien and A. Weiss, Graph congruences and wreath products, J. Pure Appl. Algebra 36 (1985) 205-215.
31. [31] B. Tilson, Categories as algebra: an essential ingredient in the theory of monoids, J. Pure Appl. Algebra 48 (1987) 83-198.
32. [32] P. Weil, Closure of varieties of languages under products with counter, J. Comput. System Sci. 45 (1992) 316-339.