Homogeneous \(p\)-differential polynomials.
type: Item
instance of: scholarly article
title: Homogeneous \(p\)-differential polynomials.
zbMATH Open document ID: 1067.12005
DOI: 10.1016/S0021-8693(03)00384-3
author: Alexandru Buium
author: Ken Zimmerman
published in: Journal of Algebra
publication date: 2003-12-04T00:00:00Z
review text: The first author earlier showed that algebraic geometry may be enlarged by adjoining a ``Fermat quotient type operation'' and the resulting geometry was named as \(\delta\)-geometry. Later he with his kolleagues introduced certain graded rings that should be interpreted as rings of sections of appropriate line bundles on the corresponding orbit spaces in \(\delta\)-geometry. In some cases these rings are isomorphic to certain subrings \(R\{x\}^{\ast}\) and \(R\{x\}_{\ast}\) of the ring \(R\{x\}\), which is an analogue of the Ritt-Kolchin ring of differential polynomials (cf. \textit{A. Buium} [Vostokov, S. (ed.) et al., Algebraic number theory and algebraic geometry. Papers dedicated to A. N. Parshin on the occasion of his sixtieth birthday. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 300, 59--97 (2002; Zbl 1084.14524)] for an overview). In the present paper the authors study the properties of this ring which is ``\(\delta\)-geometric''. In particular, the \(p\)-adic completion of a basic ring of fractions attached to \(R\{x\}_{\ast}\) is described and the analysis of homomorphisms between the basic rings is provided.
reviewed by: M. Ya. Komarnitskiy
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 12H25
zbMATH DE Number: 2013024
zbMATH Keywords: \(\delta\)-geometry
zbMATH Keywords: graded rings
zbMATH Keywords: orbit spaces
zbMATH Keywords: Ritt-Kolchin ring of differential polynomials
zbMATH Keywords: \(p\)-adic completion
zbMATH Keywords: local \(p\)-ring
zbMATH Keywords: global \(p\)-ring
zbMATH Keywords: \(p\)-differential polynomials
zbMATH Keywords: telescopic morphisms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013024