A note On 2-prime ideals

Document Type : Research Paper

Authors

Department of Mathematics, Vali-e-Asr University, Rafsanjan, Iran

Abstract

Let $R$ be a commutative ring with identity. In this paper, we study 2-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 2-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 2-prime. Finally, we define almost 2-prime, almost 2-primary and weakly 2-primary ideals, and investigate some properties of these ideals.

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References

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History

  • Receive Date: 27 June 2023
  • Revise Date: 07 January 2024
  • Accept Date: 25 February 2024

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