Puissances divisées en caractéristique non nulle. (Divided powers in non zero characteristic) (Q1109081)

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 \(Hom(A_+/A^ 2_+,A_+)\).