Quasi-maximal ideals and ring extensions

TL;DR

This paper explores quasi-maximal and submaximal ideals in ring theory, providing new characterizations and linking them to minimal extensions and 2-absorbing ideals, advancing understanding of ring extensions.

Contribution

It introduces submaximal ideals, characterizes finite minimal extensions via quasi-maximal ideals, and connects these concepts to Badawi 2-absorbing ideals.

Findings

Quasi-maximal ideals are characterized comprehensively.

Finite minimal extensions have conductors that are quasi-maximal.

Connections established between quasi-maximal ideals and 2-absorbing ideals.

Abstract

Alan and al. defined and studied quasi-maximal ideals. We add a comprehensive characterization of these ideals, introducing submaximal ideals. The conductor of a finite minimal extension $R\subset S$ is quasi-maximal in $S$. This allows us to give a new characterization of these extensions. We also examine the links between quasi-maximal ideals and Badawi 2-absorbing ideals.