On quasi n-ideals of commutative rings

A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is said to be a strongly quasi-primary ideal if, whenever [Formula: see text] with [Formula: see text], then [Formula: see text] or [Formula: see text] (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 [Formula: see text], called the class of quasi-[Formula: see text]-ideals. Among other results, this new class of ideals is used to characterize when the nil-radical of [Formula: see text] is a maximal or a minimal ideal of [Formula: see text]. Many examples are given to illustrate the obtained results.