A note On 2-prime ideals

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sharifi Vajihe; Hadjirezaei Somayeh

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Journal Paper

Paper Information

Journal: Journal of Mahani Mathematical Research Year:2024 | Volume:13 | Issue:2 Page(s): 263-273

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Information Journal Paper

Title

A note On 2-prime ideals

Author(s)

sharifi Vajihe | Hadjirezaei Somayeh | Issue Writer Certificate

Keywords

2-prime ideal

almost 2-prime ideal

almost 2-primary

Ideal

weakly 2-primary ideal

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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