Integrating Hasse-Schmidt derivations
type: Item
instance of: scholarly article
title: Integrating Hasse-Schmidt derivations
zbMATH Open document ID: 1304.13045
author: Piotr Kowalski
author: Daniel Max Hoffmann
published in: Journal of Pure and Applied Algebra
publication date: 2014-12-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1212.5788
review text: The authors study ``integrating (that is, expanding to a Hasse-Schmidt derivation) derivations and more generally truncated Hasse-Schmidt derivations (HS derivations, for short), satisfying iterativity conditions given by formal group laws''. In particular, the authors concentrate their attention on the additive and multiplicative group laws. Such formal group laws give the possibility to reinterpret classical results on derivations in a new way. On the other hand one of the main motivation of the authors ``for considering this topic'' was to study ``other theories of existentially closed fields with HS derivations''. The notion of the Hasse-Schmidt derivation was introduced by \textit{H. Hasse} and \textit{F. K. Schmidt} in 1937 [J. Reine Angew. Math. 177, 215--237 (1937; Zbl 0017.10101; JFM 63.0098.01)], under the name of ``higher derivation'', and the topic was widely studied by Hideyuki Matsumura whose results on this subject have been fundamental for the development of the algebraic theory of derivations. Indeed, the main result in the paper is a generalization of a theorem of Matsumura via group scheme actions.
reviewed by: Marilena Crupi
Mathematics Subject Classification ID: 13N15
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 6377267
zbMATH Keywords: Hasse-Schmidt derivation
zbMATH Keywords: group scheme actions
MaRDI profile type: Publication
OpenAlex ID: W1965691476
arXiv ID: 1212.5788
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DOI: 10.1016/J.JPAA.2014.05.024
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description: scientific article