JOURNAL ARTICLE

Directed partial orders on complex numbers and quaternions.

  • Published In: Journal of Algebra & Its Applications, 2025, v. 24, n. 8. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Ma, Jingjing 3 of 3

Abstract

Let D be an integral domain that is algebraic over ℤ. It is shown that each directed maximal partial order on D is an Archimedean total order. Let F be a subfield of ℝ and C = F (i) be the complex field over F. As a consequence of the above result, if F is algebraic over ℚ , then C does not have a directed partial order making it a partially ordered ring. In particular, C cannot be a lattice-ordered ring. The result is proved for certain partially ordered algebras of quaternions as well. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Algebra & Its Applications. 2025/07, Vol. 24, Issue 8, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2025
  • ISSN:0219-4988
  • DOI:10.1142/S0219498825501890
  • Accession Number:184767170
  • Copyright Statement:Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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