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Note on classification of two-dimensional associative lattice-ordered real algebras

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Abstract

In this note, we correct three non-trivial classes of Birkhoff–Pierce’s classification of two-dimensional associative lattice-ordered real algebras.

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Notes

  1. Birkhoff and Pierce (1956) only point out that \(A^+\) must contain \(e_2\), which is very vague.

  2. Birkhoff and Pierce (1956) state that \(0\le \alpha<\beta <\pi /2\), which should be corrected.

  3. Birkhoff and Pierce (1956) only list the first two possibilities of the Archimedean case, which should also be corrected.

References

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Authors and Affiliations

  1. Department of Mathematics, Beihang University, Beijing, 100191, China

    Yichuan Yang & Xiaohong Zhang

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  1. Yichuan Yang
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  2. Xiaohong Zhang
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Correspondence to Yichuan Yang.

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The authors declare that they have no conflict of interest.

Additional information

Communicated by Y. Yang.

The authors acknowledge the support of NSFC (Grant 11271040).

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Yang, Y., Zhang, X. Note on classification of two-dimensional associative lattice-ordered real algebras. Soft Comput 21, 2549–2552 (2017). https://doi.org/10.1007/s00500-017-2580-0

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  • DOI: https://doi.org/10.1007/s00500-017-2580-0

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