Rings with involution and orderings. (English) Zbl 0947.16022

The aim of the paper is to generalize the Artin-Schreier theory of ordered fields to rings with involution. The notion of ordering of a ring with involution is studied, and is related to the formation of rings of fractions in which symmetric elements are invertible.
Remarks: Some of the proofs contain gaps or errors. For example, in the proof of Theorem (17) the author claims (implicitly) that if \(M\) is a multiplicatively closed semi-ordering and \(s=s^*\notin M\) then \(M\cup-sP\cup M-sP\) is a multiplicatively closed semi-ordering. This is not true.


16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16W80 Topological and ordered rings and modules
16U20 Ore rings, multiplicative sets, Ore localization
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)