Relatively complete ordered fields without integer parts

Mojtaba Moniri, and Jafar S. Eivazloo. "Relatively complete ordered fields without integer parts." Fundamenta Mathematicae 179.1 (2003): 17-25. <http://eudml.org/doc/283315>.

@article{MojtabaMoniri2003,
abstract = {We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series $[[F^G]]$ with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that $[[F^G]]$ is always Scott complete. In contrast, the Puiseux series field with coefficients in F always has proper dense field extensions.},
author = {Mojtaba Moniri, Jafar S. Eivazloo},
journal = {Fundamenta Mathematicae},
keywords = {ordered fields; Scott complete; monotone complete; generalized power series; integer part},
language = {eng},
number = {1},
pages = {17-25},
title = {Relatively complete ordered fields without integer parts},
url = {http://eudml.org/doc/283315},
volume = {179},
year = {2003},
}

TY - JOUR
AU - Mojtaba Moniri
AU - Jafar S. Eivazloo
TI - Relatively complete ordered fields without integer parts
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 1
SP - 17
EP - 25
AB - We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series $[[F^G]]$ with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that $[[F^G]]$ is always Scott complete. In contrast, the Puiseux series field with coefficients in F always has proper dense field extensions.
LA - eng
KW - ordered fields; Scott complete; monotone complete; generalized power series; integer part
UR - http://eudml.org/doc/283315
ER -