## $$n$$-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

### Keywords:

prime ideal; $$r$$-ideal; $$n$$-ideal
Full Text:

### References:

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