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.