Relatively complete ordered fields without integer parts

• Autorzy: Mojtaba Moniri , Jafar S. Eivazloo
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13J05: Power series rings
• 12J15: Ordered fields
• 54H13: Topological fields, rings, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 1
• Strony: 17-25

Daty

wydano

2003

Twórcy

autor

Mojtaba Moniri

• Institute for Studies in Theoretical, Physics and Mathematics (IPM), Tehran, Iran

autor

Jafar S. Eivazloo

• Institute for Studies in Theoretical, Physics and Mathematics (IPM), Tehran, Iran

Identyfikatory

DOI

10.4064/fm179-1-2