Dual spaces of totally ordered rings. (English) Zbl 0671.06010

This paper continues and relies on earlier work of the author [Dual spaces of totally ordered abelian groups, ibid. 37, 613-627 (1987; Zbl 0645.06007)]. There, he assigns a dual space to every totally ordered abelian group in such a way that the evaluation map into the second dual is one-to-one and order preserving. In this paper he investigates the question whether, for totally ordered rings, convolution may be used to define a multiplication on the second dual in such a way that the evaluation map also preserves the multiplication. The author succeeds for a class of rings that include all lexicographically ordered power series rings with real coefficients on totally ordered cancellative semigroups. The precise statements of the results are too involved to be recorded here.
Reviewer: K.Keimel


06F25 Ordered rings, algebras, modules


Zbl 0645.06007
Full Text: DOI EuDML


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