Artin approximation over Banach spaces

Authors :: Guillaume Rond
Institut de Mathématiques de Marseille (I2M)
Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Source :: Communications in Algebra, Communications in Algebra, Taylor & Francis, 2020, 48 (10), pp.4214-4223. ⟨10.1080/00927872.2020.1758937⟩, Communications in Algebra, 2020, 48 (10), pp.4214-4223. ⟨10.1080/00927872.2020.1758937⟩
Publication Year :: 2020
Abstract: We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach algebra. In particular we construct an example of a commutative integral Banach algebra $R$ such that the ring of formal power series over $R$ is not flat over the ring of convergent power series over $R$.<br />To appear in Commun. Algebra

Language :: English
ISSN :: 00927872 and 15324125
Database :: OpenAIRE
Journal :: Communications in Algebra, Communications in Algebra, Taylor & Francis, 2020, 48 (10), pp.4214-4223. ⟨10.1080/00927872.2020.1758937⟩, Communications in Algebra, 2020, 48 (10), pp.4214-4223. ⟨10.1080/00927872.2020.1758937⟩
Accession number :: edsair.doi.dedup.....b1b9106d48a48f3fb6e559a64156f1f4
Full Text :: https://doi.org/10.1080/00927872.2020.1758937⟩