Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T08:16:38.159Z Has data issue: false hasContentIssue false
  • English
  • Français

Annihilator graphs and semigroups of matrices

Published online by Cambridge University Press:  17 April 2009

S. J. Quinn
S. J. Quinn
Affiliation:
Menzies Research Institute University of Tasmania, Private Bag 23, Hobart Tas 7001 Australia, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 annihilator graphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 2004

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, Vol. 1, (Rosenberg, G. and Salomaa, A., Editors) (Springer-Verlag, Berlin, 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, Berlin, 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, (Bridge, 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. and Quinn, S.J., ‘A combinatorial property of Cayley graphs and semigroups’, Semigroup Forum 66 (2003), 89–96.CrossRefGoogle Scholar
[9]Kelarev, A.V. and Quinn, S.J., ‘Directed graphs and combinatorial properties of semigroups’, J. Algebra 251 (2002), 16–26.CrossRefGoogle Scholar
[10]Lothair, M., Combinatorics on words (Addison-Wesley, Tokyo, 1982).Google Scholar
[11]Neumann, B.H., ‘A problem of Paul Erdös on groups’, J. Austral. Math. Soc. 21 (1976), 467–472.CrossRefGoogle Scholar
[12]Okniński, J., Semigroups of Matrices (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
[13]Robinson, D.J.S., A Course in the theory of groups (Springer-Verlag, New York, Berlin, 1982).CrossRefGoogle Scholar
[14]van der Waerden, B.L., Algebra, Vol. 1 (Springer-Verlag, New York, 1991).Google Scholar