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arXiv · 1810.02238

Super-multiplicativity of ideal norms in number fields

Stefano Marseglia
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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 $N(IJ) \geq N(I)N(J)$ for every pair of non-zero ideals $I$ and $J$ of every ring extension of $R$ contained in the normalization of $R$.

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Stefano Marseglia. 2018-10-04. Super-multiplicativity of ideal norms in number fields. https://doi.org/10.4064/aa181010-26-3

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