%0 Journal Article
%T I-prime ideals
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Akray, I.
%D 2016
%\ 12/01/2016
%V 4
%N 2
%P 41-47
%! I-prime ideals
%K prime ideal
%K weakly prime ideal
%K almost prime ideal
%K radical of the ideal
%R
%X 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.
%U https://jart.guilan.ac.ir/article_1998_805b509c5392f49a246ca25b4fb110a2.pdf