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Continuous homomorphisms between algebras of iterated Laurent series over a ring

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Abstract

We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of discrete data determined by the images of parameters. In similar terms, we give a criterion of invertibility of an endomorphism and provide an explicit formula for the inverse endomorphism. We also study the behavior of the higher dimensional residue under continuous homomorphisms.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Sergey O. Gorchinskiy & Denis V. Osipov

Authors
  1. Sergey O. Gorchinskiy
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  2. Denis V. Osipov
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Correspondence to Sergey O. Gorchinskiy.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 294, pp. 54–75.

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Gorchinskiy, S.O., Osipov, D.V. Continuous homomorphisms between algebras of iterated Laurent series over a ring. Proc. Steklov Inst. Math. 294, 47–66 (2016). https://doi.org/10.1134/S0081543816060031

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