Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T18:32:00.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Idempotent endomorphisms of an independence algebra of finite rank*

Published online by Cambridge University Press:  20 January 2009

Gracinda M. S. Gomes  and
John M. Howie
Gracinda M. S. Gomes
Affiliation:
Departamento de MatematicaFaculdade de CienciasUniversidade de Lisboa1700 Lisboa, Portugal
John M. Howie
Affiliation:
Mathematical InstituteUniversity of St AndrewsNorth HaughSt Andrews, Fife, KY16 9SS, Scotland
Rights & Permissions [Opens in a new window]

Abstract

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.

The result of Ballantine [1] to the effect that a singular matrix A is a product of k idempotent matrices if and only if the rank of I – A does not exceed k times the nullity of A is generalized to endomorphisms of a class of independence algebras.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 107 - 116
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Ballantyne, C. S., Products of idempotent matrices, Linear Algebra Appl. 19 (1978), 81–86.CrossRefGoogle Scholar
2.Dawlings, R. J. H., Products of idempotents in the semigroup of singular endomorphisms of a finite-dimensional vector space, Proc. Roy. Soc. Edinburgh A 91 (1981), 123–133.CrossRefGoogle Scholar
3.Erdos, J. A., On products of idempotent matrices, Glasgow Math J. 8 (1967), 118–122.Google Scholar
4.Fountain, John and Lewin, Andrew, Products of idempotent endomorphisms of an independence algebra of finite rank, Proc. Edinburgh Math. Soc. 35 (1992), 493–500.CrossRefGoogle Scholar
5.Fountain, John and Lewin, Andrew, Products of idempotent endomorphisms of an independence algebra of infinite rank, Math. Proc. Cambridge Philos. Soc. 114 (1993), 303–319.CrossRefGoogle Scholar
6.Gould, V. A. R., Endomorphism monoids of independence algebras, preprint.Google Scholar
7.Grätzer, G., Universal algebra (Van Nostrand, Princeton, 1968).Google Scholar
8.Howie, John M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
9.Howie, John M., Products of idempotents in finite full transformation semigroups, Proc. Roy. Soc. Edinburgh A 86 (1980), 243–254.Google Scholar
10.Iwahori, Nobuko, A length formula in a semigroup of mappings, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), 255–260.Google Scholar
11.Narkiewicz, W., Independence in a certain class of abstract algebras, Fund. Math. 50 (1961/1962), 333–340.CrossRefGoogle Scholar
12.Saito, T., Products of idempotents in finite full transformation semigroups, Semigroup Forum 39 (1989), 295–309.Google Scholar