# Triangular bases of integral closures

@article{Stainsby2018TriangularBO,
title={Triangular bases of integral closures},
author={Hayden Stainsby},
journal={J. Symb. Comput.},
year={2018},
volume={87},
pages={140-175}
}
• Hayden Stainsby
• Published 2018
• Mathematics, Computer Science
• J. Symb. Comput.
• In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. Let $(K, v)$ be a discrete valued field with valuation ring $\mathcal{O}$ and let $\mathfrak{m}$ be the maximal ideal. We take $f \in \mathcal{O}[x]$, a monic irreducible polynomial of degree $n$ and consider the extension $L = K[x]/(f(x))$ as well as $\mathcal{O}_{L}$ the integral closure of $\mathcal{O}$ in $L$, which we suppose to be finitely generated as an \$\mathcal{O… CONTINUE READING

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