The pseudovariety of semigroups of triangular matrices over a finite field
Jorge Almeida; Stuart W. Margolis; Mikhail V. Volkov
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)
- Volume: 39, Issue: 1, page 31-48
- ISSN: 0988-3754
Access Full Article
topAbstract
topHow to cite
topAlmeida, Jorge, Margolis, Stuart W., and Volkov, Mikhail V.. "The pseudovariety of semigroups of triangular matrices over a finite field." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 31-48. <http://eudml.org/doc/244893>.
@article{Almeida2005,
abstract = {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.},
author = {Almeida, Jorge, Margolis, Stuart W., Volkov, Mikhail V.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {triangular matrix semigroups; pseudovarieties; finite semigroups; semigroups representable by upper triangular matrices; finite pseudoidentity bases},
language = {eng},
number = {1},
pages = {31-48},
publisher = {EDP-Sciences},
title = {The pseudovariety of semigroups of triangular matrices over a finite field},
url = {http://eudml.org/doc/244893},
volume = {39},
year = {2005},
}
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
PB - EDP-Sciences
VL - 39
IS - 1
SP - 31
EP - 48
AB - 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.
LA - eng
KW - triangular matrix semigroups; pseudovarieties; finite semigroups; semigroups representable by upper triangular matrices; finite pseudoidentity bases
UR - http://eudml.org/doc/244893
ER -
References
top- [1] J. Almeida, Implicit operations on finite -trivial semigroups and a conjecture of I. Simon. J. Pure Appl. Algebra 69 (1990) 205–218. Zbl0724.08003
- [2] J. Almeida, Finite Semigroups and Universal Algebra. World Scientific (1995). Zbl0844.20039MR1331143
- [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. Zbl0993.20035
- [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. Zbl1061.20050
- [5] A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups. Amer. Math. Soc. Vol. I (1961); Vol. II (1967). Zbl0111.03403
- [6] R.S. Cohen and J.A. Brzozowski, Dot-depth of star-free events. J. Comp. Syst. Sci. 5 (1971) 1–15. Zbl0217.29602
- [7] S. Eilenberg, Automata, Languages and Machines. Academic Press, Vol. A (1974); Vol. B (1976). Zbl0317.94045
- [8] S. Eilenberg and M.P. Schützenberger, On pseudovarieties. Adv. Math. 19 (1976) 413–418. Zbl0351.20035
- [9] D. Gorenstein, Finite Groups. 2nd edition, Chelsea Publishing Company (1980). Zbl0463.20012MR569209
- [10] R.M. Guralnick, Triangularization of sets of matrices. Linear Multilinear Algebra 9 (1980) 133–140. Zbl0443.15006
- [11] K. Henckell and J.-E. Pin, 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. Zbl0946.20031
- [12] P. Higgins, A proof of Simon’s theorem on piecewise testable languages. Theor. Comp. Sci. 178 (1997) 257–264. Zbl0901.68093
- [13] E.R. Kolchin, On certain concepts in the theory of algebraic matrix groups. Ann. Math. 49 (1948) 774–789. Zbl0037.18801
- [14] G. Lallement, Semigroups and Combinatorial Applications. John Wiley & Sons (1979). Zbl0421.20025MR530552
- [15] H. Neumann, Varieties of groups. Springer-Verlag (1967). Zbl0251.20001MR215899
- [16] J. Okniński, Semigroup of Matrices. World Scientific (1998). MR1785162
- [17] J.-E. Pin, Variétés de langages formels. Masson, 1984 [French; Engl. translation: Varieties of formal languages. North Oxford Academic (1986) and Plenum (1986)]. Zbl0636.68093MR752695
- [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 Bolyai 39, North-Holland (1985) 259–272. Zbl0635.20028
- [19] H. Radjavi and P. Rosenthal, Simultaneous Triangularization. Springer-Verlag (2000). Zbl0981.15007MR1736065
- [20] J. Reiterman, The Birkhoff theorem for finite algebras. Algebra Universalis 14 (1982) 1–10. Zbl0484.08007
- [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. Zbl0316.68034
- [23] J. Stern, Characterization of some classes of regular events. Theor. Comp. Sci. 35 (1985) 17–42. Zbl0604.68066
- [24] H. Straubing, On finite -trivial monoids. Semigroup Forum 19 (1980) 107–110. Zbl0435.20036
- [25] H. Straubing, Finite semigroup varieties of the form . J. Pure Appl. Algebra 36 (1985) 53–94. Zbl0561.20042
- [26] H. Straubing and D. Thérien, Partially ordered finite monoids and a theorem of I. Simon. J. Algebra 119 (1988) 393–399. Zbl0658.20035
- [27] D. Thérien, Classification of finite monoids: the language approach. Theor. Comp. Sci. 14 (1981) 195–208. Zbl0471.20055
- [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. Zbl0572.20052
- [29] M.V. Volkov, On a class of semigroup pseudovarieties without finite pseudoidentity basis. Int. J. Algebra Computation 5 (1995) 127–135. Zbl0834.20058
- [30] M.V. Volkov and I.A. Goldberg, Identities of semigroups of triangular matrices over finite fields. Mat. Zametki 73 (2003) 502–510 [Russian; Engl. translation: Math. Notes 73 (2003) 474–481]. Zbl1064.20056
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.