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Two-Dimensional Lattice-Ordered Algebras over ℝ -Revisit
Department of Mathematical, Applied and Physical Sciences, University of Houston-Clear Lake, Houston, TX, USA
- 1 Department of Mathematical, Applied and Physical Sciences, University of Houston-Clear Lake, Houston, TX, USA
Advances in Pure Mathematics·Volume 16 (2026)·Pages 332–340·Published 30 April 2026·DOI10.4236/apm.2026.164017
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Abstract
In this paper, it is first pointed out that the enumeration of two-dimensional lattice-ordered real algebras provided by Birkhoff and Pierce is complete. Then we classify lattice-ordered algebra F × F over a totally ordered field F . Finally in section 4, we provide more information on the partially ordered rings in which every square is positive, especially a characterization of partially ordered fields in which every square is positive is given.
KeywordsDirect Product-AlgebraSquares Positive-Basis
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