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Research Article | Open Access

Dedekind σ-complete partially ordered rings

Department of Mathematical, Applied and Physical Sciences, University of Houston-Clear Lake, 2700 Bay Area Blvd., Houston TX 77058, USA
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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

ArchimedeanDedekind σ-completeidempotentinfinite primemaximal partial orderstrong Archimedeantotal order

References

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Electronic Research Archive
Volume 34 Issue 6,
May 2026
Pages 3643-3654
DOI: 10.3934/era.2026164

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Cite this article:
Ma J. Dedekind σ-complete partially ordered rings. Electronic Research Archive, 2026, 34(6): 3643-3654. https://doi.org/10.3934/era.2026164

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Received: 07 March 2026
Revised: 13 April 2026
Accepted: 20 April 2026
Published: 29 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)