Continuous homomorphisms between algebras of iterated Laurent series over a ring

TL;DR

This paper characterizes continuous homomorphisms between algebras of iterated Laurent series over a ring, providing explicit descriptions, invertibility criteria, and analyzing residue behavior.

Contribution

It offers a complete description of such homomorphisms, including invertibility conditions and explicit inverse formulas, advancing understanding of their algebraic structure.

Findings

Described continuous homomorphisms via discrete data

Established invertibility criteria for endomorphisms

Analyzed the behavior of higher-dimensional residues

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 a 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 study the behavior of the higher-dimensional residue under continuous homomorphisms.