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Directed Partial Orders on F(i) with 1 > 0

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Abstract

Let F be a non-archimedean o-field and C be the field of generalized complex numbers over F. In this paper, we describe all the directed partial orders on C with 1 > 0 by using admissible semigroups of F +.

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References

  1. Birkhoff, G., Pierce, R.S.: Lattice-ordered rings. An. Acad. Brasil. Ci. 28, 41–69 (1956)

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  3. Ma, J., Wu, L., Zhang, Y.: Directed partial orders on generalized complex numbers and quaternions over non-archmedean linearly ordered fields, order (2016). https://doi.org/10.1007/s11083-016-9387-y

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Authors and Affiliations

  1. Department of Mathematics, University of Houston-Clear Lake, 2700 Bay Area Boulevard, Houston, TX, 77058, USA

    Jingjing Ma

  2. College of Engineering, Nanjing Agricultural University, Nanjing, 210095, China

    Liusan Wu

  3. School of Information Management, Nanjing University, 163 Xianlin Road, Nanjing, 210023, China

    Liusan Wu

  4. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240, Shanghai, China

    Yuehui Zhang

Authors
  1. Jingjing Ma
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  2. Liusan Wu
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  3. Yuehui Zhang
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Corresponding author

Correspondence to Yuehui Zhang.

Additional information

Yuehui Zhang is supported by NSFC under Grant No. 11671258 and 11771280, by NSF of Shanghai Municipal under Grant No. 13ZR1422500 and 14ZR1415400.

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Ma, J., Wu, L. & Zhang, Y. Directed Partial Orders on F(i) with 1 > 0. Order 35, 461–466 (2018). https://doi.org/10.1007/s11083-017-9442-3

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  • DOI: https://doi.org/10.1007/s11083-017-9442-3

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