Quasi-maximal ideals and ring extensions

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.