• STRONG GOLDIE DIMENSION AND KRULL DIMENSION OF MODULES

Abstract

Let R be an associative ring with identity. A unital right R-module M is said to be of strong Goldie dimension n (written SG.dim M = n) if sup {G.dim (M/N) | N ≤ M} = n. Otherwise, we set SG.dimM = +∞. A module M is called strongly finite dimensional if SG.dim M < +∞, where G.dim denotes the Goldie dimension of a module. In this paper we attempt to provide a new insight to characterize strongly finite dimensional module. Some equivalent conditions are obtained regarding finite Goldie dimension and Krull dimension. It  has been proved  that if M  be a serial module  having  no 0-critical  submodule , then M is strongly  finite dimensional  if and  only if M has Krull dimension. Using the concepts of strong Goldie dimension and Krull dimension, extending modules are characterized.