Lattice-ordered matrix algebras over real GCD-domains

Fei Li; Xianlong Bai; Derong Qiu

doi:10.1080/00927872.2011.654299

Lattice-ordered matrix algebras over real GCD-domains

Rings and Algebras 2014-07-02 v5 Number Theory

Authors: Fei Li , Xianlong Bai , Derong Qiu

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Abstract

Let $R \subset \R$ be a GCD-domain. In this paper, Weinberg's conjecture on the $n \times n$ matrix algebra $M_{n}(R) \ (n \geq 2)$ is proved. Moreover, all the lattice orders (up to isomorphisms) on a full $2 \times 2$ matrix algebra over $R$ are obtained.

Keywords

lattice theory hadamard matrices graded algebras

Cite

@article{arxiv.1010.4380,
  title  = {Lattice-ordered matrix algebras over real GCD-domains},
  author = {Fei Li and Xianlong Bai and Derong Qiu},
  journal= {arXiv preprint arXiv:1010.4380},
  year   = {2014}
}

Comments

9 pages, this is the final version (to appear in the Journal: Communications in Algebra). Thanks to the anonymous referee's helpful suggestions, we replace the UFD rings by the GCD-domains in this paper

Lattice-ordered matrix algebras over real GCD-domains

Abstract

Keywords

Cite

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