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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
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Abstract

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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

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