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**Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings.**
*(English)*
Zbl 1299.16020

A ring \(R\) is called a near pseudo-valuation ring if every minimal prime ideal of \(R\) is strongly prime. Now let \(\sigma\) be an automorphism of \(R\) and let \(\delta\) be a \(\sigma\)-derivation of \(R\). Then \(R\) is called an almost \(\delta\)-divided ring if every minimal prime ideal of \(R\) is \(\delta\)-divided.

In the present paper the author studies the question when a Noetherian ring \(R\), which is also an algebra over the field of rational numbers, is either a near pseudo-valuation ring or an almost \(\delta\)-divided ring, where \(\delta\) is a \(\sigma\)-derivation of \(R\) with the automorphism \(\sigma\).

In the present paper the author studies the question when a Noetherian ring \(R\), which is also an algebra over the field of rational numbers, is either a near pseudo-valuation ring or an almost \(\delta\)-divided ring, where \(\delta\) is a \(\sigma\)-derivation of \(R\) with the automorphism \(\sigma\).

Reviewer: Adalbert Bovdi (Debrecen)

### MSC:

16S36 | Ordinary and skew polynomial rings and semigroup rings |

16D25 | Ideals in associative algebras |

16P40 | Noetherian rings and modules (associative rings and algebras) |

16W60 | Valuations, completions, formal power series and related constructions (associative rings and algebras) |

### Keywords:

Ore extensions; automorphisms; derivations; minimal prime ideals; strongly prime ideals; near pseudo-valuation rings### References:

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