A note On ۲-prime ideals

Let R be a commutative ring with identity. In this paper, we study ۲-prime ideals of a Dedekind domain and a Pr\"{u}fer domain. We prove that a nonzero ideal I of a Dedekind domain R is ۲-prime if and only if I=P^{\alpha}, for some maximal ideal P of R and positive integer \alpha. We give some results of ring R in which every ideal I is ۲-prime. Finally, we define almost ۲-prime, almost ۲-primary and weakly ۲-primary ideals, and investigate some properties of these ideals.

کلیدواژه ها:

۲-prime ideal ، almost ۲-prime ideal ، almost ۲-primary ، Ideal ، weakly ۲-primary ideal