Akray, I. \(I\)-prime ideals. (English) Zbl 1355.13003 J. Algebra Relat. Top. 4, No. 2, 41-47 (2016). Summary: 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. Cited in 2 ReviewsCited in 5 Documents MSC: 13A15 Ideals and multiplicative ideal theory in commutative rings Keywords:prime ideal; weakly prime ideal; almost prime ideal; radical of the ideal PDFBibTeX XMLCite \textit{I. Akray}, J. Algebra Relat. Top. 4, No. 2, 41--47 (2016; Zbl 1355.13003) Full Text: arXiv Link