On quasi-n-ideals of commutative rings

A proper ideal I of a commutative ring R is said to be a strongly quasi-primary ideal v ' if, whenever a, b epsilon R with ab epsilon I, then a(2)epsilon I or b epsilon vI (see [S. Koc, U. Tekir and G. Ulucak, On strongly quasi primary ideals, Bull. Korean Math. Soc. 56(3) (2019) 729-743]). This paper studies the class of strongly quasi-primary ideals with a radical equal to the nil-radical of R, called the class of quasi-n-ideals. Among other results, this new class of ideals is used to characterize when the nil-radical of R is a maximal or a minimal ideal of R. Many examples are given to illustrate the obtained results.