The Factorization of $p$ in $\mathbf{Q}(a^{1/p^k})$ and the Genus Field of $\mathbf{Q}(a^{1/n})$

VÉLEZ, William Yslas

Tokyo J. of Math., Tome 11 (1988) no. 2, p. 1-19 / Harvested from Project Euclid

Résumé

Let $x^{p^k}-a$ be irreducible over $\mathbf{Q}$. The first part of this paper is to explicitly give the decomposition rules for the factorization of $p$ in the ring of integers of $\mathbf{Q}(a^{1/p^k})$. ¶ As an application of the above we use these results to determine the genus field of $\mathbf{Q}(a^{1/n})$, where $x^n-a$ is irreducible over $\mathbf{Q}$ and we make no restrictions on $a$.

Publié le : 1988-06-15
Classification:

@article{1270134258,
     author = {V\'ELEZ, William Yslas},
     title = {The Factorization of $p$ in $\mathbf{Q}(a^{1/p^k})$ and the Genus Field of $\mathbf{Q}(a^{1/n})$},
     journal = {Tokyo J. of Math.},
     volume = {11},
     number = {2},
     year = {1988},
     pages = { 1-19},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270134258}
}

VÉLEZ, William Yslas. The Factorization of $p$ in $\mathbf{Q}(a^{1/p^k})$ and the Genus Field of $\mathbf{Q}(a^{1/n})$. Tokyo J. of Math., Tome 11 (1988) no. 2, pp.  1-19. http://gdmltest.u-ga.fr/item/1270134258/