Noetherian Skew Inverse Power Series Rings

2007/03/19 by Edward S. Letzter, Linhong Wang, Letzter, Edward S. +1
Mathematics · #16L30 #16S36 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16L30 #msc:16S36

paper · pdf · doi:10.48550/arxiv.math/0703558

12 pages; no figures. Revised; to appear in Algebras and Representation Theory

openalex publication_date 2007/03/19 · arxiv created 2008/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study skew inverse power series extensions R[[y^-1;tau,delta]], where R is a noetherian ring equipped with an automorphism tau and a tau-derivation delta. We find that these extensions share many of the well known features of commutative power series rings. As an application of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete local, noetherian, Auslander regular domains whose right Krull dimension, global dimension, and classical Krull dimension, are all equal to 2n.

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• S-Noetherian generalized power series rings
• Bounded skew power series rings for inner σ-derivations
• Dimension theory in iterated local skew power series rings
• Reduced Archimedean skew polynomial rings and skew power series rings
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