SUPPLEMENTS IN COATOMIC MODULES HAVING THE COMPLETE MAX-PROPERTY

Abstract

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.

Keywords

• Coatomic module,completely coindependent,complete max- property,good module,maximal submodule

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