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We study continuous homomorphisms between algebras of iterated Laurent seriesover a commutative ring. We give a full description of such homomorphisms interms of a discrete data determined by the images of parameters. In similarterms, we give a criterion of invertibility of an endomorphism and provide anexplicit formula for the inverse endomorphism. We study the behavior of thehigher-dimensional residue under continuous homomorphisms.

Continuous homomorphisms between algebras of iterated Laurent series over a ring