@article { author = {Akray, I.}, title = {I-prime ideals}, journal = {Journal of Algebra and Related Topics}, volume = {4}, number = {2}, pages = {41-47}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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.}, keywords = {prime ideal,weakly prime ideal,almost prime ideal,radical of the ideal}, url = {https://jart.guilan.ac.ir/article_1998.html}, eprint = {https://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdf} }