Abstract
Let L = K(α) be an extension of a number field K where α satisfies the monic irreducible polynomial P(X) = Xp −a ∈ R[X] of prime degree p and such that a is pth power free in R := OK (the ring of integers of K). The purpose of this paper is to give an explicit formula for the ideal discriminant DL/K of L over K involving only the prime ideals dividing the principal ideals aR and pR. As an illustration, we compute the discriminant DL/K of a family of septic and quintic pure fields over quadratic fields. Hence a slightly simpler computation of discriminant DL/K is obtained.
Publisher
Sociedade Paranaense de Matemática
Reference26 articles.
1. Atiyah. M. F, Macdonald. I. G., Introduction to Commutative Algebra. Addison-Wesley, Massachusetts, (1969).
2. Cassels. J. W. S, Fröhlich. A., Algebraic Number Theory, Academic Press, London and New york, 1967.
3. M. E. Charkani, O. Lahlou, On Dedekind's criterion and monogenicity over Dedekind rings. Int. J. of Math. and Math. Sci. (2003)
4. (7) (2003) 4455-4464. Zbl 1066.11046, https://doi.org/10.1155/S0161171203211534.
5. M. E. Charkani, A. Deajim, Generating a power basis over a Dedekind Ring. J. Number Theory 132, No. 10, 2267-2276, (2012).Zbl 1293.11101, https://doi.org/10.1016/j.jnt.2012.04.006.