THE NAKAYAMA PROPERTY OF A MODULE AND RELATED CONCEPTS

Three related properties of a module are investigated in this article, namely the Nakayama property, the Maximal property, and the S-property. A module M has the Nakayama property if alpha M = M for an ideal alpha implies that sM = 0 for some s is an element of alpha + 1. A module M has the Maximal property if there is in M a maximal proper submodule, and finally, M is said to have the S-property if S-1M = 0 for a multiplicatively closed set S implies that sM = 0 for some s is an element of S.