Resumen de Characterizations of 0-submodules

Félix Marcelo Wirnitzer, César Rodríguez Mielgo

• In this paper we give an introduction to prime submodules in order to generalize the concept of prime ideal to the category of modules. First of all, we study prime submodules of ideal 0 in the case where the ring is an integral domain. For this reason we ha ve called these submodules 0 submodules. We show several properties of these submodules are torsion free. This result allows us to apply local cohomology to characterize 0- submodules of rank one of reflexive modules over the polynomial ring in n variables as free modules. Second, we develop two theorems which define a bijection between objects.