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Power graphs and semigroups of matrices

Published online by Cambridge University Press:  17 April 2009

A. V. Kelarev ,
S. J. Quinn  and
R. Smolíková
A. V. Kelarev
Affiliation:
Department of Mathematics, University of Tasmania, G.P.O. Box 252–37Hobart Tas. 7001, Australia e-mail: [email protected]
S. J. Quinn
Affiliation:
Department of Electrical Engineering, University of Louisville, United States of America, e-mail: [email protected]
R. Smolíková
Affiliation:
Department of Mathematics, University of Tasmania, Launceston Tas 7250, Australia e-mail: [email protected]
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Abstract

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Matrices provide essential tools in many branches of mathematics, and matrix semigroups have applications in various areas. In this paper we give a complete description of all infinite matrix semigroups satisfying a certain combinatorial property defined in terms of power graphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 341 - 344
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Chartland, G. and Lesniak, L., Graphs and digraphs (Chapman & Hall, London, 1996).Google Scholar
[2]de Luca, A. and Varricchio, S., ‘Regularity and finiteness conditions’, in Handbook of Formal Languages 1, (Rosenberg, G. and Salomaa, A., Editors) (Springer-Verlag, Berlin, Heidelberg, New York, 1997), pp. 747–810.CrossRefGoogle Scholar
[3]de Luca, A. and Varricchio, S., Finiteness and regularity in semigroups and formal languages, Monographs in Theoretical Computer Science (Springer-Verlag, Berlin, Heidelberg, New York, 1998).Google Scholar
[4]Howie, J.M., Fundamentals of semigroup theory (Clarendon Press, Oxford, 1995).CrossRefGoogle Scholar
[5]Jespers, E. and Okniński, J., ‘On a class of Noetherian algebras’, Proc. Roy. Soc. Edinburgh Sect.A 129 (1999), 1185–1196.CrossRefGoogle Scholar
[6]Justin, J. and Pirillo, G., ‘On some questions and conjectures in combinatorial semigroup theory’, Southeast Asian Bull. Math. 18 (1994), 91–104.Google Scholar
[7]Kelarev, A. V., ‘Combinatorial properties of sequences in groups and semigroups’, in Combinatorics, Complexity and Logic, (Bridges, D.S., Calude, C.S., Gibbons, J., Reeves, S. and Witten, I.H., Editors), Springer Ser. Discrete Math. Theor. Comput. Soc. (Springer-Verlag, Singapore, 1997), pp. 289–298.Google Scholar
[8]Kelarev, A. V., ‘Radicals of algebras graded by cancellative linear semigroups’, Proc. Amer. Math. Soc. 124 (1996), 61–65.CrossRefGoogle Scholar
[9]Kelarev, A.V. and Quinn, S.J., ‘A combinatorial property of power graphs of groups’, in Contrib. General Algebra 12 (Heyn, Klagenfurt, 2000), pp. 229–235.Google Scholar
[10]Lidl, R. and Pilz, G., Applied abstract algebra (Springer-Verlag, Berlin, Heidelberg, New York, 1998).CrossRefGoogle Scholar
[11]Lothair, M., Combinatorics on words (Addision-Wesley, Tokyo, 1982).Google Scholar
[12]Neumann, B.H., ‘A problem of Paul Erdös on groups’, J. Austral. Math. Soc. 21 (1976), 467–472.CrossRefGoogle Scholar
[13]Okniński, J., Semigroups of matrices (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
[14]Robinson, D.J.S., A Course in the theory of groups (Springer-Verlag, Berlin, Heidelberg, New-York, 1982).CrossRefGoogle Scholar