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Super-multiplicativity of ideal norms in number fields

Volume 193 / 2020

Stefano Marseglia 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 $\tilde R$.

Authors

  • Stefano MarsegliaDepartment of Mathematics
    Stockholm University
    SE-106 91 Stockholm, Sweden
    e-mail

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