Super-multiplicativity of ideal norms in number fields
Volume 193 / 2020
Acta Arithmetica 193 (2020), 75-93
MSC: Primary 13A15; Secondary 11R21, 11R54.
DOI: 10.4064/aa181010-26-3
Published online: 2 January 2020
Abstract
We study inequalities of ideal norms. We prove that in a subring $R$ of a number field every ideal can be generated by at most three elements if and only if the ideal norm satisfies $N(IJ)\geq N(I)N(J)$ for every pair of non-zero ideals $I$ and $J$ of every ring extension of $R$ contained in the normalization $\tilde R$.
