Dedekind σ-complete partially ordered rings

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Abstract

In this paper, I present the properties and structures of Dedekind σ-complete directed partially ordered rings and algebras over R. Under certain conditions, such as property P₁, chain conditions on convex ideals, and strong Archimedean, structures are isomorphic to the real number field R with the usual total order or finite product or subdirect product of R.

Keywords

Archimedean / Dedekind σ-complete / idempotent / infinite prime / maximal partial order / strong Archimedean / total order

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