Preprint
Sep 2026
On the index of generalized trinomials over Valued fields
Let $\nu$ be a Krull valuation of arbitrary rank on a field with valuation ring $R_\nu$, and let $\theta$ be a root of the irreducible polynomial $F(x)=(x^k+c)^m-ax^n\in R_\nu[x]$ and $1\leq n<km$. We establish necessary and sufficient conditions for the integral closedness of $R_\nu[\theta]$, expressed explicitly in t...
V. Adithya
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