Puissances divisées en caractéristique non nulle. (Divided powers in non zero characteristic)
type: Item
instance of: scholarly article
title: Puissances divisées en caractéristique non nulle. (Divided powers in non zero characteristic)
zbMATH Open document ID: 0655.13007
DOI: 10.1016/0021-8693(87)90064-0
author: Jean Pierre Soublin
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The paper contains many results about divided algebras of positive characteristic. It is proved that on a divided algebra there exists a logarithm. The author refines a theorem of \textit{H. Cartan} [Sem. H. Cartan 1954/1955'' (Paris 1956)] by describing necessary and sufficient conditions for the existence of a system of divided powers on a pregraduated \({\mathbb{F}}_ p\)-algebra A (p is prime). He discusses the special case \(A=k[X]/(X^ p)\), where k is a commutative field of positive characteristic p. It is finally established a parametrization of the structures of divided algebras on \(A=A_ 0\oplus A_+\) by the elements of the module \(Hom(A_+/A^ 2_+,A_+)\).
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13J05
Mathematics Subject Classification ID: 11T99
zbMATH DE Number: 4069033
zbMATH Keywords: power series
zbMATH Keywords: divided algebra
zbMATH Keywords: logarithm
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90064-0
OpenAlex ID: W2006502602
cites work: Q5521581
cites work: Construction de certaines algèbres à puissances divisées
description: scientific article; zbMATH DE number 4069033