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Let be a uniformly complete almost -algebra and a natural number . Then is a uniformly complete semiprime -algebra under the ordering and multiplication inherited from with as positive cone.
This work provides an evaluating complete description of positive homomorphisms on an arbitrary algebra of real-valued functions.
This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost -rings introduced again by Birkhoff.
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