Super-multiplicativity of ideal norms in number fields

Abstract

In this article 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 $3$ elements if and only if the ideal norm satisfies $N(IJ)\ge N(I)N(J)$ for every pair of non-zero ideals $I$ and $J$ of every ring extension of $R$ contained in the normalization of $R$.

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Cited by in corpus (2)

• Cohen-Macaulay type of orders, generators and ideal classes
• Ray class groups and ray class fields for orders of number fields