Note on strongly quasi-primary ideals

Abstract

Let [Formula: see text] be a commutative ring with [Formula: see text]. A proper ideal [Formula: see text] of [Formula: see text] is said to be a strongly quasi-primary ideal if, whenever [Formula: see text] with [Formula: see text], then either [Formula: see text] or [Formula: see text]. In this paper, we characterize Noetherian and reduced rings over which every (respectively, nonzero) proper ideal is strongly quasi-primary. We also characterize ring over which every strongly quasi primary ideal of [Formula: see text] is prime. Many examples are given to illustrate the obtained results.