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- W4387410130 abstract "AbstractThe main goal of this paper is to calculate the index of any number field K generated by a root of an irreducible trinomial x4+ax+b∈Z[x]. Our approach is based on Engstrom’s results and the factorization of 2ZK and 3ZK. In particular, we reformulate the Davis and Spearman’s results. Namely, for every prime integer p, we evaluate νp(i(K)). The existence of a common index divisor of K guaranties the non monogenity of K.KEYWORDS: Common index divisorpower integral basesprime ideal factorizationtheorem of ore2020 MATHEMATICS SUBJECT CLASSIFICATION: 11R0411Y4011R21 AcknowledgmentsThe author is deeply grateful to the Editor Adrian Wadsworth for his guidance, to the anonymous referee whose valuable comments and suggestions have tremendously improved the quality of this paper, as well as to Professor István Gaál for his encouragement and advice, and to Professor Enric Nart who introduced him to Newton’s polygon techniques." @default.
- W4387410130 created "2023-10-07" @default.
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- W4387410130 date "2023-10-06" @default.
- W4387410130 modified "2023-10-08" @default.
- W4387410130 title "A note on indices of quartic number fields defined by trinomials <i>x</i> <sup>4</sup> + <i>ax</i> + <i>b</i>" @default.
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- W4387410130 doi "https://doi.org/10.1080/00927872.2023.2262041" @default.
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