Orderings and preorderings in rings with involution
Volume 83 / 2000
Colloquium Mathematicum 83 (2000), 15-20
DOI: 10.4064/cm-83-1-15-20
Abstract
The notions of a preordering and an ordering of a ring R with involution are investigated. An algebraic condition for the existence of an ordering of R is given. Also, a condition for enlarging an ordering of R to an overring is given. As for the case of a field, any preordering of R can be extended to some ordering. Finally, we investigate the class of archimedean ordered rings with involution.
