Geodesic
Algebraic integers with discriminants containing fixed prime divisors
Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 289-296 
L. A. Trelina. Algebraic integers with discriminants containing fixed prime divisors. Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 289-296. http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a0/
@article{MZM_1977_21_3_a0,
     author = {L. A. Trelina},
     title = {Algebraic integers with discriminants containing fixed prime divisors},
     journal = {Matemati\v{c}eskie zametki},
     pages = {289--296},
     year = {1977},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a0/}
}
TY  - JOUR
AU  - L. A. Trelina
TI  - Algebraic integers with discriminants containing fixed prime divisors
JO  - Matematičeskie zametki
PY  - 1977
SP  - 289
EP  - 296
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a0/
LA  - ru
ID  - MZM_1977_21_3_a0
ER  - 
%0 Journal Article
%A L. A. Trelina
%T Algebraic integers with discriminants containing fixed prime divisors
%J Matematičeskie zametki
%D 1977
%P 289-296
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a0/
%G ru
%F MZM_1977_21_3_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that any algebraic integer $\alpha$ of degree $n\ge2$ whose discriminant is a product of powers of prescribed primes $p_1,\dots,p_r$ has the form $\alpha=a+\beta p_1^{v_1}\dotsp_r^{v_r}$, where $\alpha,v_1,\dots,v_r$ are rational integers and $\beta$ is an integer whose height does not exceed an effectively defined bound depending $\max(p1,\dots,p_r)$, $r$, and $n$.