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Lattice-Ordered Matrix Rings Over Totally Ordered Rings

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Abstract

For an n ×n matrix algebra over a totally ordered integral domain, necessary and sufficient conditions are derived such that the entrywise lattice order on it is the only lattice order (up to an isomorphism) to make it into a lattice-ordered algebra in which the identity matrix is positive. The conditions are then applied to particular integral domains. In the second part of the paper we consider n ×n matrix rings containing a positive n-cycle over totally ordered rings. Finally a characterization of lattice-ordered matrix ring with the entrywise lattice order is given.

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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. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yuehui Zhang

Authors
  1. Jingjing Ma
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  2. Yuehui Zhang
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Correspondence to Jingjing Ma.

Additional information

Yuehui Zhang is supported by NSFC, Grant No. 11271257.

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Ma, J., Zhang, Y. Lattice-Ordered Matrix Rings Over Totally Ordered Rings. Order 31, 45–54 (2014). https://doi.org/10.1007/s11083-013-9287-3

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  • DOI: https://doi.org/10.1007/s11083-013-9287-3

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