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BIBTEX RIS

Some properties of ideals in rings of power series

1944; American Mathematical Society; Volume: 55; Linguagem: Inglês

10.1090/s0002-9947-1944-0010548-x

ISSN

1088-6850

Autores

Claude Chevalley,

Tópico(s)

Advanced Topics in Algebra

Resumo

The behavior of a prime ideal in a polynomial ring when the basic field is extended to a larger field has been studied extensively by Zariski(l) in the case of a basic field of characteristic 0 and by A. Weil in the general case (his results are not published as yet).Our main purpose is to extend these results to the case of ideals in rings of power series, a case in which essentially new difficulties are encountered.We have nevertheless included in this paper a treatment of the "polynomial" case; several types of arguments appear in their simplest form in this case.1. Separably generated extensions.A finite extension Z/K of a field K

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