Second modules relative to subclasses of preradicals of $R$-Mod

Abstract

We study the concept of second module and extend it to more general environments. We also provide descriptions of simple left semiartinian, left local rings, semisimple and simple rings in terms of their $\mathscr A$-second modules with respect to a preradical class.

Keywords

• R-pr
• A-second module
• strongly second module
• left semiartinian
• left local ring

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