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\(n\)-ideals of commutative rings. (English) Zbl 1488.13016

Summary: In this paper, we present a new classes of ideals: called \(n\)-ideal. Let \(R\) be a commutative ring with nonzero identity. We define a proper ideal \(I\) of \(R\) as an \(n\)-ideal if whenever \(ab \in I\) with \(a \not\in \sqrt{0}\), then \(b \in I\) for every \(a,b \in R\). We investigate some properties of \(n\)-ideals analogous with prime ideals. Also, we give many examples with regard to \(n\)-ideals.

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
13A99 General commutative ring theory
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