Orderings, valuations, and Hermitian forms over *-fields

Ordered ∗-Rings

“…Considerable work has been done on the topic of orderings on skew fields with involution ( * -fields), with several different generalizations of the usual ordering on a commutative field being considered (see the survey article [Cr3] for references). Recently Marshall [M] has extended the theory of * -orderings on * -fields to the case of general rings with involution ( * -rings).…”

Hermitian Forms over Ordered ∗ -Fields

“…Much more can be accomplished in the case of ordered fields and for this reason, Holland [H2, H3] has worked with Baer's original definition of an ordering for * -fields and extensions of that definition to obtain a tractable noncommutative setting. A survey of the work of many authors on ordered * -fields can be found in [Cr6].…”