The pseudovariety of semigroups of triangular matrices over a finite field

 Access to full text

 Full (PDF)

1. J. Almeida, Implicit operations on finite J-trivial semigroups and a conjecture of I. Simon. J. Pure Appl. Algebra69 (1990) 205–218.  
2. J. Almeida, Finite Semigroups and Universal Algebra. World Scientific (1995).  
3. J. Almeida and A. Azevedo, Globals of pseudovarieties of commutative semigroups: the finite basis problem, decidability, and gaps. Proc. Edinburgh Math. Soc.44 (2001) 27–47.  
4. J. Almeida and M.V. Volkov, Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl.2 (2003) 137–163.  
5. A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups. Amer. Math. Soc. Vol. I (1961); Vol. II (1967).  
6. R.S. Cohen and J.A. Brzozowski, Dot-depth of star-free events. J. Comp. Syst. Sci.5 (1971) 1–15.  
7. S. Eilenberg, Automata, Languages and Machines. Academic Press, Vol. A (1974); Vol. B (1976).  
8. S. Eilenberg and M.P. Schützenberger, On pseudovarieties. Adv. Math.19 (1976) 413–418.  
9. D. Gorenstein, Finite Groups. 2nd edition, Chelsea Publishing Company (1980).  
10. R.M. Guralnick, Triangularization of sets of matrices. Linear Multilinear Algebra9 (1980) 133–140.  
11. K. Henckell and J.-E. Pin, Ordered monoids and J-trivial monoids, in Algorithmic problems in groups and semigroups, edited by J.-C. Birget, S. Margolis, J. Meakin and M. Sapir. Birkhäuser (2000) 121–137.  
12. P. Higgins, A proof of Simon's theorem on piecewise testable languages. Theor. Comp. Sci.178 (1997) 257–264.  
13. E.R. Kolchin, On certain concepts in the theory of algebraic matrix groups. Ann. Math.49 (1948) 774–789.  
14. G. Lallement, Semigroups and Combinatorial Applications. John Wiley & Sons (1979).  
15. H. Neumann, Varieties of groups. Springer-Verlag (1967).  
16. J. Okniński, Semigroup of Matrices. World Scientific (1998).  
17. J.-E. Pin, Variétés de langages formels. Masson, 1984 [French; Engl. translation: Varieties of formal languages. North Oxford Academic (1986) and Plenum (1986)].  
18. J.-E. Pin and H. Straubing, Monoids of upper triangular matrices, in Semigroups. Structure and Universal Algebraic Problems, edited by G. Pollák, Št. Schwarz and O. Steinfeld. Colloquia Mathematica Societatis János Bolyai39, North-Holland (1985) 259–272.  
19. H. Radjavi and P. Rosenthal, Simultaneous Triangularization. Springer-Verlag (2000).  
20. J. Reiterman, The Birkhoff theorem for finite algebras. Algebra Universalis14 (1982) 1–10.  
21. I. Simon, Hierarchies of Events of Dot-Depth One. Ph.D. Thesis, University of Waterloo (1972).  
22. I. Simon, Piecewise testable events, in Proc. 2nd GI Conf.Lect. Notes Comp. Sci.33 (1975) 214–222.  
23. J. Stern, Characterization of some classes of regular events. Theor. Comp. Sci.35 (1985) 17–42.  
24. H. Straubing, On finite J-trivial monoids. Semigroup Forum19 (1980) 107–110.  
25. H. Straubing, Finite semigroup varieties of the form V ∗ D. J. Pure Appl. Algebra36 (1985) 53–94.  
26. H. Straubing and D. Thérien, Partially ordered finite monoids and a theorem of I. Simon. J. Algebra119 (1988) 393–399.  
27. D. Thérien, Classification of finite monoids: the language approach. Theor. Comp. Sci.14 (1981) 195–208.  
28. D. Thérien, Subword counting and nilpotent groups, in Combinatorics on Words, Progress and Perspectives, edited by L.J. Cummings. Academic Press (1983) 297–305.  
29. M.V. Volkov, On a class of semigroup pseudovarieties without finite pseudoidentity basis. Int. J. Algebra Computation5 (1995) 127–135.  
30. M.V. Volkov and I.A. Goldberg, Identities of semigroups of triangular matrices over finite fields. Mat. Zametki73 (2003) 502–510 [Russian; Engl. translation: Math. Notes73 (2003) 474–481].