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Orderings and preorderings in rings with involution. (English) Zbl 0961.16020
The notion of an ordering on a general ring was described by L. Fuchs [Fundam. Math. 46, 167-174 (1959; Zbl 0100.26701)] and the notion of an ordered skew field with involution was studied by M. Chacron [J. Algebra 75, 495-522 (1982; Zbl 0482.16013)] and 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.

MSC:
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
06F25 Ordered rings, algebras, modules
16W80 Topological and ordered rings and modules
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