On Classical Prime Near-ring Modules

TL;DR

This paper extends the concept of classical prime modules from rings to near-ring modules, defining and analyzing various types, and exploring properties like annihilators and classical m-systems.

Contribution

It introduces multiple types of classical prime modules in near-ring modules and investigates their properties, expanding the theory beyond classical ring modules.

Findings

Defined and distinguished four types of classical prime modules.

Proved properties related to annihilators of these modules.

Characterized classical m-systems of R-ideals in near-ring modules.

Abstract

In 2005, M. Behboodi introduced the notion of a classical prime ring module, which he showed is, in general, nonequivalent to a (Dauns) prime ring module. In this paper, we extended the idea of classical primeness to near-ring module. However, unlike in the ring case, we were able to define and distinguish between various types of classical prime modules. We investigate four of them here. We also prove some properties about the annihilator. Finally we characterize the classical $m$-systems of $R$-ideals of near-ring modules.