Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T06:53:34.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Products of idempotents in regular rings

Published online by Cambridge University Press:  18 May 2009

K. C. O'Meara
K. C. O'Meara
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand
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.

The problem of describing the subsemigroup generated by the idempotents in various natural semigroups has received the attention of several semigroup theorists ([1], [2], [3], [5], [7]). However, in those cases where the parent semigroup is in fact the multiplicative semigroup of a natural ring, the known ring structure has not been exploited. When this ring structure is taken into account, proofs can often be streamlined and can lead to more general arguments (such as not requiring that the elements of the semigroup be already transformations of some known structure).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 143 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Dawlings, R. J. H., Products of idempotents in the semigroup of singular endomorphisms of a finite-dimensional vector space, Proc. Roy. Soc. Edinburgh Sect. A 91 (1981), 123–133.CrossRefGoogle Scholar
2.Dawlings, R. J. H., The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 351–360.CrossRefGoogle Scholar
3.Erdos, J. A., On products of idempotent matrices, Glasgow Math. J. 8 (1967), 118–122.CrossRefGoogle Scholar
4.Goodearl, K. R., Von Neumann regular rings (Pitman, 1979).Google Scholar
5.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
6.O'Meara, K. C., Right orders in full linear rings, Ph.D. Thesis, University of Canterbury (1971)Google Scholar
7.Reynolds, M. A. and Sullivan, R. P., Products of idempotent linear transformations, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 123–138.CrossRefGoogle Scholar