Discrete ordered rings
G. Heuer (1974)
Fundamenta Mathematicae
Similarity:
G. Heuer (1974)
Fundamenta Mathematicae
Similarity:
Ulrich Albrecht, Günter Törner (1998)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
James J. Madden (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
Similarity:
Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational...
Ismail M. Idris (2001)
Colloquium Mathematicae
Similarity:
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as...
Carlton J. Maxson (1970)
Compositio Mathematica
Similarity:
R.H. Redfield (1986)
Manuscripta mathematica
Similarity:
Paulo Ribenboim (1995)
Collectanea Mathematica
Similarity:
Joan Pairó (1983)
Fundamenta Mathematicae
Similarity: