Abstract
Let R he a commutative ring with 1 not equal 0. A proper ideal I of R is said to be a strongly quasi-primary ideal if, whenever a,b is an element of R with ab is an element of I, then either a(2) is an element of I or b is an element of root I. 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 R is prime. Many examples are given to illustrate the obtained results.