ISMAIL M. IDRIS

Orderings and preorderings in rings with involution

Pages: 119-125
Received: 15 March 1999   
Mathematics Subject Classification: 16K40 - 16W10

Abstract: The notion of an ordering of a field was studied by Artin and Schreler. One can ask now if this can be generalized to noncommutative rings with involut-.on. In this paper, the notions of a preordering and an ordering of a ring R with involution is investigateci. 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 preorderinc, of R can be extended to some ordering. Finally, we establish a classification theorem for archimedean ordered rings with involution. We should remark that the orderings as defined in this work can only exist for rings without zero-divisors.