We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series 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 is always Scott complete. In contrast, the Puiseux series field with coefficients in F always has proper dense field extensions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-2,
author = {Mojtaba Moniri and Jafar S. Eivazloo},
title = {Relatively complete ordered fields without integer parts},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {17-25},
zbl = {1083.12004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-2}
}
Mojtaba Moniri; Jafar S. Eivazloo. Relatively complete ordered fields without integer parts. Fundamenta Mathematicae, Tome 177 (2003) pp. 17-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-2/