Dedekind's criterion and Integral bases

Year, pages: 2019, 1 - 8

Let $R$ be a principal ideal domain with quotient field $K$, and $L=K(α)$, where $α$ is a root of a monic irreducible polynomial $F(x)\in R[x]$. Let $\mathbb Z_L$ be the integral closure of $R$ in $L$. In this paper, for every prime $p$ of $R$, we give a new efficient version of Dedekind's criterion in $R$, i.e., necessary and sufficient conditions on $F(x)$ to have $p$ not dividing the index $[\mathbb Z_L:R[α]]$, for every prime $p$ of $R$. Some computational examples are given for $R=\mathbb Z$.

El Fadil, L. 2019. Dedekind's criterion and Integral bases. In Tatra Mountains Mathematical Publications, vol. 73, no.1, pp. 1-8. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0001

El Fadil, L. (2019). Dedekind's criterion and Integral bases. Tatra Mountains Mathematical Publications, 73(1), 1-8. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0001

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

© 2019 Mathematical Institute, Slovak Academy of Sciences. Licensed under the Creative Commons Attribution-NC-ND 4.0 International Public License.