On Regular Modules over Commutative Rings.

In this paper, we investigate the class of von Neumann regular modules over commutative rings. More precisely, we introduce a characterization of regular modules, and then, we study some properties of these modules in viewpoint of this characterization. Among other things, we show that the Nakayama's Lemma and Krull's intersection theorem hold for this class of modules. Also, some explicit expressions for submodules of regular modules are introduced. [ABSTRACT FROM AUTHOR]