The Dedekind completion of \(d\)-algebras. (English) Zbl 1073.46002
Summary: It is shown that the multiplication in an Archimedean \(d\)-algebra \(A\) can be extended to a multiplication in the Dedekind completion \(A^{\delta}\) of \(A\) such that \(A^{\delta}\) becomes a \(d\)-algebra with respect to this extended multiplication. This answers a question posed by C. B. Huijsmans [Stud. Econ. Theory 2, 151–169 (1991; Zbl 0789.06012)].
MSC:
| 46A40 | Ordered topological linear spaces, vector lattices |
| 06F25 | Ordered rings, algebras, modules |
| 47B65 | Positive linear operators and order-bounded operators |
Citations:
Zbl 0789.06012References:
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