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