English

Super-multiplicativity of ideal norms in number fields

Number Theory 2022-01-19 v2

Abstract

In this article we study inequalities of ideal norms. We prove that in a subring RR of a number field every ideal can be generated by at most 33 elements if and only if the ideal norm satisfies N(IJ)N(I)N(J)N(IJ) \geq N(I)N(J) for every pair of non-zero ideals II and JJ of every ring extension of RR contained in the normalization of RR.

Keywords

Cite

@article{arxiv.1810.02238,
  title  = {Super-multiplicativity of ideal norms in number fields},
  author = {Stefano Marseglia},
  journal= {arXiv preprint arXiv:1810.02238},
  year   = {2022}
}

Comments

Final version. The content is the same as the "Online First" version published on the journal's web site