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Additive matrix maps that are monotone with respect to the orders induced by the group inverse

Abstract

We characterize additive maps on the matrix algebra over an arbitrary field with three or more elements that are monotone with respect to the \( \mathop{\leq}\limits^{\#} \)- and \( \mathop{\leq}\limits^{\mathrm{cn}} \)-orders and build some examples of nonadditive monotone maps.

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Correspondence to M. A. Efimov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 6, pp. 23–40, 2011/12.

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Efimov, M.A. Additive matrix maps that are monotone with respect to the orders induced by the group inverse. J Math Sci 193, 659–670 (2013). https://doi.org/10.1007/s10958-013-1493-4

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Keywords

  • Regular Semigroup
  • Invertible Matrix
  • Additive Subgroup
  • Group Inverse
  • Nonzero Scalar