# $I$-prime ideals

## TL;DR

This paper introduces the concept of $I$-prime ideals as a generalization of weakly prime ideals in commutative rings, providing characterizations, properties, and conditions for their relation to prime and weakly prime ideals.

## Contribution

It defines $I$-prime ideals, explores their properties, and establishes conditions linking them to prime and weakly prime ideals in decomposite rings.

## Key findings

- $I$-prime ideals generalize weakly prime ideals.
- Characterizations of $I$-prime ideals are provided.
- Conditions for $I$-prime ideals to be prime or weakly prime are established.

## Abstract

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b \in R$ with $ab \in P-IP$ implies either $a \in P$ or $b \in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.