Systèmes de puissances partiellement divisées. (French) Zbl 0563.13013

The purpose of this paper is to introduce and to initiate the study of a generalization of algebra with divided powers. The new system of operations is defined under certain restrictions on the ring: essentially, the latter is assumed to be an algebra over a DVR, which is a finite extension of the localization of the integers at some fixed prime p. The precise set of conditions which is to be satisfied by the partially divided powers is too technical to be stated here: it is sufficient to note that for different choices of the paramters involved in the definition, one can obtain the ordinary powers as well as the usual divided ones. The second half of the paper is devoted to applications of this construction to the study of polynomial functors of vector spaces over an infinite field, and of Clifford algebras over a field of characteristic different from two.


13F99 Arithmetic rings and other special commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
15A66 Clifford algebras, spinors
13A10 Radical theory on commutative rings (MSC2000)
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