# Continuous homomorphisms between algebras of iterated Laurent series over a ring

```@article{Gorchinskiy2016ContinuousHB,
title={Continuous homomorphisms between algebras of iterated Laurent series over a ring},
author={S. Gorchinskiy and Denis Vasilievich Osipov},
journal={Proceedings of the Steklov Institute of Mathematics},
year={2016},
volume={294},
pages={47-66}
}```
• Published 24 April 2016
• Mathematics
• Proceedings of the Steklov Institute of Mathematics
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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We construct a higher-dimensional Contou-Carrère symbol and we study some of its fundamental properties. The higher-dimensional Contou-Carrère symbol is defined by means of the boundary map for
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