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On mappings whose sum is monotone


Proposition 1 of this article points at a gap in the proof of Kuhlmann’s characterization of algebraically maximal valued fields [2]. The author [1] showed how to fill this gap. His arguments involved tools of mathematical logic and infinite combinatorics. Proposition 2 of this article provides us with a simple proof of the key fact of Kuhlmann’s characterization.

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  1. 1.

    Yu. L. Ershov, Multi-valued Fields (Kluwer Academic Publ./Consultants Bureau, New York, 2001).

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  2. 2.

    F.-V. Kuhlmann, Valuation Theory of Fields, Abelian Groups and Modules, Habilitation (Universität Heidelberg, Heidelberg, 1994).

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  3. 3.

    F.-V. Kuhlmann, “Elementary properties of power series fields over finite fields,” J. Symbolic Logic 66(2), 771–791 (2001).

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Correspondence to Yu. L. Ershov.

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Original Russian Text © Yu. L. Ershov, 2004, published in Vestnik NGU. Matematika, Mekhanika, Informatika, 2004, Vol. IV, No. 1, pp. 19–21.

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Ershov, Y.L. On mappings whose sum is monotone. Sib. Adv. Math. 21, 259–261 (2011).

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  • linearly ordered Abelian groups
  • valued fields