Note on classification of two-dimensional associative lattice-ordered real algebras
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In this note, we correct three non-trivial classes of Birkhoff–Pierce’s classification of two-dimensional associative lattice-ordered real algebras.
KeywordsAssociative lattice-ordered real algebra Archimedean Non-Archimedean
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The authors declare that they have no conflict of interest.
- Birkhoff G (1967) Lattice theory, 3rd edn. American Mathematical Society Colloquium Publications, Vol XXV. American Mathematical Society, Providence, R.IGoogle Scholar
- Birkhoff G, Maclane S (1953) Survey of modern algebra, revised ednGoogle Scholar
- DeMarr R, Steger A (1972) On elements with negative squares. Proc AMS 31:57–60Google Scholar
- Schwartz N, Yang Y. Archimedean partially ordered fields (Preprint) Google Scholar
- Vaida D (2017) An extension of a Y. C. Yang theorem. Soft Comput. doi: 10.1007/s00500-017-2578-7
- Yang Y (2006a) On the existence of directed rings and algebras with negative squares. J Algebra 295:452–457Google Scholar
- Yang Y (2006b) A lattice-ordered skew field is totally ordered if squares are positive. Am Math Mon 113(3):265–266Google Scholar
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