an:01496205
Zbl 0961.16020
Idris, Ismail M.
Orderings and preorderings in rings with involution
EN
Colloq. Math. 83, No. 1, 15-20 (2000).
00062973
2000
j
16W10 06F25 16W80
Archimedean rings; orderings; rings with involutions; extendibility; symmetric elements; commutative subrings
The notion of an ordering on a general ring was described by \textit{L. Fuchs} [Fundam. Math. 46, 167-174 (1959; Zbl 0100.26701)] and the notion of an ordered skew field with involution was studied by \textit{M. Chacron} [J. Algebra 75, 495-522 (1982; Zbl 0482.16013)] and \textit{S. S. Holland} [J. Algebra 101, 16-46 (1986; Zbl 0624.06024)]. The author defines an ordering on a general ring with involution and establishes the expected conditions for its existence and extendibility to overrings. He also shows that when the ring is Achimedean, the symmetric elements generate a commutative subring.
Paul M.Cohn (London)
Zbl 0100.26701; Zbl 0482.16013; Zbl 0624.06024