We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
@article{ITA_2005__39_1_31_0, author = {Almeida, Jorge and Margolis, Stuart W. and Volkov, Mikhail V.}, title = {The pseudovariety of semigroups of triangular matrices over a finite field}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {31--48}, publisher = {EDP-Sciences}, volume = {39}, number = {1}, year = {2005}, doi = {10.1051/ita:2005002}, mrnumber = {2132577}, zbl = {1086.20029}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2005002/} }
TY - JOUR AU - Almeida, Jorge AU - Margolis, Stuart W. AU - Volkov, Mikhail V. TI - The pseudovariety of semigroups of triangular matrices over a finite field JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 31 EP - 48 VL - 39 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2005002/ DO - 10.1051/ita:2005002 LA - en ID - ITA_2005__39_1_31_0 ER -
%0 Journal Article %A Almeida, Jorge %A Margolis, Stuart W. %A Volkov, Mikhail V. %T The pseudovariety of semigroups of triangular matrices over a finite field %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 31-48 %V 39 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2005002/ %R 10.1051/ita:2005002 %G en %F ITA_2005__39_1_31_0
Almeida, Jorge; Margolis, Stuart W.; Volkov, Mikhail V. The pseudovariety of semigroups of triangular matrices over a finite field. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 31-48. doi : 10.1051/ita:2005002. http://www.numdam.org/articles/10.1051/ita:2005002/
[1] Implicit operations on finite -trivial semigroups and a conjecture of I. Simon. J. Pure Appl. Algebra 69 (1990) 205-218. | Zbl
,[2] Finite Semigroups and Universal Algebra. World Scientific (1995). | MR | Zbl
,[3] Globals of pseudovarieties of commutative semigroups: the finite basis problem, decidability, and gaps. Proc. Edinburgh Math. Soc. 44 (2001) 27-47. | Zbl
and ,[4] Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl. 2 (2003) 137-163. | Zbl
and ,[5] The Algebraic Theory of Semigroups. Amer. Math. Soc. Vol. I (1961); Vol. II (1967). | Zbl
and ,[6] Dot-depth of star-free events. J. Comp. Syst. Sci. 5 (1971) 1-15. | Zbl
and ,[7] Automata, Languages and Machines. Academic Press, Vol. A (1974); Vol. B (1976). | Zbl
,[8] On pseudovarieties. Adv. Math. 19 (1976) 413-418. | Zbl
and ,[9] Finite Groups. 2nd edition, Chelsea Publishing Company (1980). | MR | Zbl
,[10] Triangularization of sets of matrices. Linear Multilinear Algebra 9 (1980) 133-140. | Zbl
,[11] Ordered monoids and -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. | Zbl
and ,[12] A proof of Simon's theorem on piecewise testable languages. Theor. Comp. Sci. 178 (1997) 257-264. | Zbl
,[13] On certain concepts in the theory of algebraic matrix groups. Ann. Math. 49 (1948) 774-789. | Zbl
,[14] Semigroups and Combinatorial Applications. John Wiley & Sons (1979). | MR | Zbl
,[15] Varieties of groups. Springer-Verlag (1967). | MR | Zbl
,[16] Semigroup of Matrices. World Scientific (1998). | MR
,[17] Variétés de langages formels. Masson, 1984 [French; Engl. translation: Varieties of formal languages. North Oxford Academic (1986) and Plenum (1986)]. | MR | Zbl
,[18] 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 Bolyai 39, North-Holland (1985) 259-272. | Zbl
and ,[19] Simultaneous Triangularization. Springer-Verlag (2000). | MR | Zbl
and ,[20] The Birkhoff theorem for finite algebras. Algebra Universalis 14 (1982) 1-10. | Zbl
,[21] Hierarchies of Events of Dot-Depth One. Ph.D. Thesis, University of Waterloo (1972).
,[22] Piecewise testable events, in Proc. 2nd GI Conf. Lect. Notes Comp. Sci. 33 (1975) 214-222. | Zbl
,[23] Characterization of some classes of regular events. Theor. Comp. Sci. 35 (1985) 17-42. | Zbl
,[24] On finite -trivial monoids. Semigroup Forum 19 (1980) 107-110. | Zbl
,[25] Finite semigroup varieties of the form . J. Pure Appl. Algebra 36 (1985) 53-94. | Zbl
,[26] Partially ordered finite monoids and a theorem of I. Simon. J. Algebra 119 (1988) 393-399. | Zbl
and ,[27] Classification of finite monoids: the language approach. Theor. Comp. Sci. 14 (1981) 195-208. | Zbl
,[28] Subword counting and nilpotent groups, in Combinatorics on Words, Progress and Perspectives, edited by L.J. Cummings. Academic Press (1983) 297-305. | Zbl
,[29] On a class of semigroup pseudovarieties without finite pseudoidentity basis. Int. J. Algebra Computation 5 (1995) 127-135. | Zbl
,[30] Identities of semigroups of triangular matrices over finite fields. Mat. Zametki 73 (2003) 502-510 [Russian; Engl. translation: Math. Notes 73 (2003) 474-481]. | Zbl
and ,Cité par Sources :