Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T04:05:30.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Modules with Finite Spanning Dimension

Published online by Cambridge University Press:  20 November 2018

K. M. Rangaswamy
K. M. Rangaswamy*
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, CanberraA.C.T. 2600, Australia University of Papua New Guinea, Port Moresby Papua New Guinea
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.

Modules with finite spanning dimension were defined by P. Fleury [3] in an attempt to dualize the concept of Goldie dimension. In this note we study these modules in some detail, obtain an improved structure theorem for them and also extend the work done in [2] and [3]. Projective modules with finite spanning dimension turn out to be local or artinian.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 255 - 262
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bass, H., Finitistic dimension and a homological generalisation of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488.Google Scholar
2. Fleury, P., Hollow modules and local endomorphism rings, Pacific J. Math. 53 (1974), 379-385.Google Scholar
3. Fleury, P., A note on dualizing Goldie dimension, Canadian Math. Bulletin, 17 (1974), 511-517.Google Scholar
4. Harada, M., On semi-simple abelian categories, Osaka J. Math. 7 (1970), 89-95.Google Scholar
5. Kaplansky, I., Modules over Dedekind domains and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327-340.Google Scholar
6. Kasch, F. and Mares, E. A., Eine Kennzeichnung semi-perfecter Moduln, Nagoya Math. J. 27 (1966), 525-529.Google Scholar
7. Lambek, J., Lectures on rings and modules, Toronto, Blaisdell Publ. Co., 1966.Google Scholar
8. Rangaswamy, K. M. and Vanaja, N., Quasi-projectives in abelian and module categories, Pacific J. Math. 43 (1972), 221-238.Google Scholar
9. Ware, R., Endomorphism rings of projective modules, Trans. Amer. Math. Soc. 155 (1971), 233-256.Google Scholar