On common index divisors and monogenity of septic number fields defined by trinomials of type \(x^7 + ax^2 + b\) (Q6548001)
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scientific article; zbMATH DE number 7857904
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On common index divisors and monogenity of septic number fields defined by trinomials of type \(x^7 + ax^2 + b\) |
scientific article; zbMATH DE number 7857904 |
Statements
On common index divisors and monogenity of septic number fields defined by trinomials of type \(x^7 + ax^2 + b\) (English)
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31 May 2024
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The author studies the field index \(i(K)\) and monogenity properties of number fields \(K\) generated by a root of an irreducible trinomial \(x^7+ax^2+b\). It is shown that 2 can be the only prime divisor of \(i(K)\). Necessary and sufficient conditions are given for \(a,b\) so that 2 divides \(i(K)\). The proofs use the standard method of Newton polygons.
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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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