Title of article :
SUPPLEMENTS IN COATOMIC MODULES HAVING THE COMPLETE MAX-PROPERTY
Author/Authors :
Demba Cisse, Mame Departement de Math´emathiques et Informatique - Faculte des Sciences et Techniques - Universit´e Cheikh Anta Diop, senegal , Ngom, Lamine Departement de Math´emathiques et Informatique - Faculte des Sciences et Techniques - Universit´e Cheikh Anta Diop, senegal , Sow, Djiby Departement de Math´emathiques et Informatique - Faculte des Sciences et Techniques - Universit´e Cheikh Anta Diop, senegal
Abstract :
Let R be a ring with identity. A right R-module M has the complete max-property if the maximal submodules of M are completely coindependent (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 maxproperty. 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
Journal title :
International Electronic Journal of Algebra
