Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T02:21:52.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructing lattice-ordered fields and division rings

Published online by Cambridge University Press:  17 April 2009

R.H. Redfield
R.H. Redfield
Affiliation:
Department of Mathematics and Computer ScienceHamilton CollegeClinton NY13323United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Neumann's totally ordered power series fields and division rings may be tipped over to form archimedean lattice-ordered fields and division rings. This process is described and then generalised to produce non-archimedean lattice-ordered fields and division rings in which 1 > 0 and, as well, ones in which 1 ≯ 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 365 - 369
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Conrad, Paul, ‘Generalized semigroup rings’, J. Indian Math. Soc. 21 (1957), 73–95.Google Scholar
[2]Conrad, Paul, Lattice Ordered Groups (Mathematics Department, Tulane University, New Orleans, USA, 1970).Google Scholar
[3]Conrad, Paul and Dauns, John, ‘An embedding theorem for lattice-ordered fields’, Pacific J. Math. 30 (1969), 385–398.CrossRefGoogle Scholar
[4]Conrad, Paul, Harvey, John and Holland, Charles, ‘The Hahn embedding theorem for lattice-ordered groups’, Trans. Amer. Math. Soc. 108 (1963), 143–169.CrossRefGoogle Scholar
[5]Neumann, B.H., ‘On ordered division rings’, Trans. Amer. Math. Soc. 66 (1949), 202–252.CrossRefGoogle Scholar
[6]Redfield, R.H., ‘Embeddings into power series rings’, submitted.Google Scholar
[7]Ribenboim, Paulo, Commutative Convolution Rings of Ordered Monoids (Preprint, Mathematics Department, Queen's University, Kingston, Canada, 1988).Google Scholar