a note on 2-prime ideals

Let r be a commutative ring with identity. in this paper, we study 2-prime ideals of a dedekind domain and a prüfer domain. we prove that a nonzero ideal i of a dedekind domain r is 2-prime if and only if i = pα, for some maximal ideal p of r and positive integer α. we give some results of ring r in which every ideal i is 2-prime. finally, we define almost 2-prime, almost 2-primary and weakly 2-primary ideals, and investigate some properties of these ideals.