Is there an infinite field whose multiplicative group is indecomposable?
Number Theory
2022-04-22 v1
Abstract
In an earlier paper, we determined the finite fields with indecomposable multiplicative groups and conjectured that there is no infinite field whose multiplicative group is indecomposable. In this paper, we prove this conjecture for several popular classes of fields, including finitely generated fields, discrete valued fields, fields of Hahn series, local fields, global fields, and function fields.
Keywords
Cite
@article{arxiv.2204.10146,
title = {Is there an infinite field whose multiplicative group is indecomposable?},
author = {Sunil K. Chebolu and Keir Lockridge},
journal= {arXiv preprint arXiv:2204.10146},
year = {2022}
}
Comments
6 pages, to appear in the Indian Journal of Pure and Applied Mathematics