Beta G-Star Relation on Modules

Abstract

In this work, we say submodules X and Y of M are 13; equivalence, X beta*Y-g, if and only if Y + K = M for every K <= M such that X + K = M and X + T = M for every T <= M such that Y+T = M. It is proved that the 39 relation is an equivalent relation and has good behaviour with respect to addition of submodules and homomorphisms.