Composition of Bhargava's Cubes over Number Fields

TL;DR

This paper extends Bhargava's cube composition to the ring of integers in certain number fields, broadening the understanding of algebraic structures beyond the rational numbers.

Contribution

It generalizes Bhargava's cube composition law to number fields with narrow class number one, excluding totally imaginary fields, thus expanding the algebraic framework.

Findings

Generalization of cube composition to new number fields

Identification of conditions excluding totally imaginary fields

Potential applications to algebraic number theory

Abstract

In this paper, the composition of Bhargava's cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields.