Truncation In Unions of Hahn Fields with a Derivation
Logic
2016-11-01 v1 Commutative Algebra
Classical Analysis and ODEs
Abstract
Truncation in Generalized Series fields is a robust notion, in the sense that it is preserved under various algebraic and some transcendental extensions. In this paper, we study conditions that ensure that a truncation closed set extends naturally to a truncation closed differential ring, and a truncation closed differential field has a truncation closed Liouville closure. In particular, we introduce the Notion of IL-closedness in Unions of Hahn fields in order to determine that this condition is sufficient to preserve truncation in those two settings for constructions such as the field of logarithmic-exponential transseries.
Keywords
Cite
@article{arxiv.1610.10058,
title = {Truncation In Unions of Hahn Fields with a Derivation},
author = {Santiago Camacho},
journal= {arXiv preprint arXiv:1610.10058},
year = {2016}
}