First elements associated with partial order actions in $R$-Mod

Abstract

We explore some concepts of module theory that derive from the notion of primeness, such as first modules, and extend them to more general environments. We also provide descriptions of simple left semiartinian rings, left local rings, semisimple rings, and simple rings in terms of their $\mathcal{A}$-first modules with respect to a preradical class.

16 pages