Super-multiplicativity of ideal norms in number fields

DOI10.4064/AA181010-26-3zbMATH Open1453.11141arXiv1810.02238OpenAlexW3106196121WikidataQ126411955 ScholiaQ126411955MaRDI QIDQ5220104

Stefano Marseglia

Publication date: 10 March 2020

Published in: Acta Arithmetica (Search for Journal in Brave)

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

Full work available at URL: https://arxiv.org/abs/1810.02238

zbMATH Keywords

number fieldnumber ringideal norm

Mathematics Subject Classification ID

Other number fields (11R21) Ideals and multiplicative ideal theory in commutative rings (13A15) Other algebras and orders, and their zeta and (L)-functions (11R54)

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