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Let R be a ring with identity. A right R-module M has the com- plete max-property if the maximal submodules of M are completely coindepen- dent (i.e., every maximal submodule of M does not contain the intersection of the other maximal submodules of M). A right R-module is said to be a good module provided every proper submodule of M containing Rad(M) is an intersection of maximal submodules of M. We obtain a new characterization of good modules. Also, we study good modules which have the complete max- property. The second part of this paper is devoted to investigate supplements in a coatomic module which has the complete max-property.

SUPPLEMENTS IN COATOMIC MODULES HAVING THE COMPLETE MAX-PROPERTY