Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T14:23:05.936Z Has data issue: false hasContentIssue false
  • English
  • Français

Modules with finite spanning dimension

Published online by Cambridge University Press:  09 April 2009

Bhavanari Satyanarayana
Bhavanari Satyanarayana
Affiliation:
Department of Mathematics, Nagarjuna University, Nagarjuna Nagar - 522510, Andra Pradesh, India
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.

It is well known that if M is a module with finite spanning dimension, then one can talk of Sd(K), the spanning dimension of K only when K is a supplement submodule in M. In this paper we extend this concept to general submodules and obtained some important results. We characterize the set of all supplement submodules of the module R/(x) over R where R is a Euclidean domain and x ∈ R. Moreover, it is proved that the number of distinct supplements in R/(x) is 2k and Sd(R/(x)) = k where k is the number of distinct nonassociate prime factors of x.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 170 - 178
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Fleury, P., ‘A note on dualizing Goldie dimension’, Canad. Math. Bull. 17 (1974), 511–517.CrossRefGoogle Scholar
[2]Herstein, I. N., Topics in algebra, 2nd edition (Vikas Publishing House, 1983).Google Scholar
[3]Satyanarayana, Bh., ‘On modules with finite spanning dimension’, Proc. Japan Acad. Ser. A Math. Sci. 61A (1985), 23–25.CrossRefGoogle Scholar
[4]Satyanarayana, Bh., ‘On modules with FSD and a property (P)’, in: Proc. Ramanujan Centennial International Conference, Annamalai Nagar, 15–18 December (1987) pp. 137–140.Google Scholar
[5]Satyanarayana, Bh., ‘A note on E-direct and S-inverse systems’, Proc. Japan Acad. Ser. A Math. Sci. 64A (1988), 292–295.CrossRefGoogle Scholar