On ordered division rings

• Autorzy: Ismail M. Idris
• Języki publikacji: EN

Abstrakty

EN

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 in the commutative case. Further, we show that the bounded subring associated with that ordering is a valuation ring which is preserved under conjugation, so one can associate with the semiordering a natural valuation.

Kategorie tematyczne

• 16W10: Rings with involution; Lie, Jordan and other nonassociative structures
• 06F25: Ordered rings, algebras, modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 88
• Numer: 2
• Strony: 263-271

Daty

wydano

2001

Twórcy

autor

Ismail M. Idris

• Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt

Identyfikatory

DOI

10.4064/cm88-2-8