On the existence of special quasifields
type: Item
instance of: scholarly article
title: On the existence of special quasifields
zbMATH Open document ID: 0723.12010
DOI: 10.1007/BF01198647
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: This note is devoted to the construction of planar quasifields \((Q,+,\cdot)\) having the following special properties: Q is formally- real, it admits an ordering the natural place ring of which is not invariant, the rational numbers lie in the centre of Q, and the rule \((- x)y=-(xy)\) does not hold in Q. In view of the latter properties, a question of \textit{H. Wähling} [Theorie der Fastkörper (Essen 1987; Zbl 0669.12014), problem 2, p. 14] is answered in the negative.
Mathematics Subject Classification ID: 12K99
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51G05
zbMATH DE Number: 4191840
zbMATH Keywords: planar quasifields
zbMATH Keywords: formally-real
zbMATH Keywords: ordering
author: Franz B. Kalhoff
reviewed by: Franz B. Kalhoff
MaRDI profile type: Publication
cites work: Über angeordnete Fastkörper
cites work: Witt rings of weakly orderable double loops and nearfields
cites work: Formal power series over Cartesian groups and their spaces of orderings
cites work: Angeordnete Fastkörper
cites work: Q3223453
cites work: The Banach fixed point theorem for ultrametric spaces
cites work: Q3822294
full work available at URL: https://doi.org/10.1007/bf01198647
OpenAlex ID: W2015277941
Recommended article: On quasifields
Recommended article: Q3726889
Recommended article: Q5593035
Recommended article: A note on places of quasifields
Recommended article: About special elements in quaternion algebras over finite fields
Recommended article: On the exceptional fields for a class of real quadratic fields
Recommended article: Q4714255
Recommended article: Q5325562
Recommended article: Q4440929
description: scientific article; zbMATH DE number 4191840