Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-31T01:27:55.149Z Has data issue: false hasContentIssue false
  • English
  • Français

The projective geometry arising from a hollow module

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Jeremy E. Dawson
Jeremy E. Dawson
Affiliation:
CSIRO Division of Mathematics and Statistics P. O. Box 218 Lindfield, NSW 2070, Australia
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.

We discuss the projective geometry defined in terms of the hollow factor modules of a given module. In particular, we derive an explicit expression for the division ring obtained in coordinatizing such a projective geometry.

MSC classification

Secondary: 05B35: Matroids, geometric lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 3 , December 1984 , pp. 351 - 357
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Anderson, F. W. & Fuller, K. R., Rings and categories of modules (Springer-Verlag, New York, 1973).Google Scholar
[2]Dawson, J. E., ‘Independence spaces and uniform modules’, European J. Combinatorics, to appear.Google Scholar
[3]Dawson, J. E., ‘Independence spaces on the submodules of a module’, European J. Combinatorics, to appear.Google Scholar
[4]Fleury, P., ‘Hollow modules and local endomorphism rings’, Pacific J. Math. 53 (1974), 379–385.CrossRefGoogle Scholar
[5]Grätzer, G., General lattice theory (Birkhaüser, Basel, 1978).CrossRefGoogle Scholar
[6]Ware, R., ‘Endomorphism rings of projective modules’, Trans. Amer. Math. Soc. 155 (1971), 233–256.CrossRefGoogle Scholar
[7]Welsh, D. J. A., Matroid theory (Academic Press, London, 1976).Google Scholar