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- W2894735612 abstract "Let $R$ be a Dedekind ring, $mathfrak{p}$ a nonzero prime ideal of $R$, $Pin R[X]$ a monic irreducible polynomial, and $K$ the quotient field of $R$. We give in this paper a lower bound for the $mathfrak{p}$-adic valuation of the index of $P$ over $R$ in terms of the degrees of the monic irreducible factors of the reduction of $P$ modulo $mathfrak{p}$. As an important application, when the lower bound is greater than zero for some $mathfrak{p}$, we conclude that no root of $P$ generates a power integral basis in the field extension of $K$ defined by $P$." @default.
- W2894735612 created "2018-10-12" @default.
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- W2894735612 date "2018-10-06" @default.
- W2894735612 modified "2023-09-23" @default.
- W2894735612 title "Polynomial Index in Dedekind Rings" @default.
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- W2894735612 doi "https://doi.org/10.48550/arxiv.1810.02985" @default.
- W2894735612 hasPublicationYear "2018" @default.
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