On the index of the octic number field defined by \(x^8 + ax + b\) (Q6057437)
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scientific article; zbMATH DE number 7745824
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the index of the octic number field defined by \(x^8 + ax + b\) |
scientific article; zbMATH DE number 7745824 |
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On the index of the octic number field defined by \(x^8 + ax + b\) (English)
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4 October 2023
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The authors consider monogenity propeties of the number field generated by a root of the irreducible trinomial \(F(x)=x^8+ax+b\). They show that the index of the field (the ggt of the indices of primitive integers in the field) is either 1 or it is a power of 2. Necessary and sufficient conditions are given for 2 to be a divisor of the index of the field. Sufficient conditions are given for the non-monogenity of the field. The authors use Newton polygon method.
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monogenity
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power integral basis
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theorem of Ore
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prime ideal factorization
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common index divisor
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