J Austral Math Soc Ser A 57 pp170--178, 1994.

Modules with Finite Spanning Dimension

Bhavanari Satyanarayana

Abstract

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 supplememnt submodules of the module R/(x) over R where R is a Euclidean domain and x Î R. Moreover, it is proved that the number of distinct supplements in R/(x) is 2^k and Sd(R/(x)) = k where k is the number of distinct nonassiciate prime factors of x.

1991 AMS Subject Classification: 16A34, 16A53, 16A64

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Authors

Bhavanari Satyanarayana

Department of Mathematics, Nagarjuna University, Nagarjuna Nagar - 522 510, Andra Pradesh, India.