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- Title
Dimension de l'anneau des polynomes a valeurs entieres.
- Authors
Cahen, Paul-Jean
- Abstract
Let A be a commutative domain with quotient field K and A the ring of integer-valued polynomials thus A={f∈K[X]; f(A)⊂A}; we show that the Krull dimension of A is such that dim A≥dim A[X]-1 and give examples where dim A=dim A[X]-1. Considering chains of primes of A above a maximal ideal m of finite residue field, we give also examples where the length of such a chain can arbitrarily be prescribed (whereas in A[X] the length of such chains is always 1). To provide such examples we consider a pair of domains A⊂B sharing an ideal I such that A/I is finite; we give sufficient conditients to have A⊂B[X] and show that in this case dim A=dim B[X]. At last, as a generalisation of Noetherian rings of dimension 1, we consider domains with an ideal I such that A/I is finite and a power I of I is contained in a proper principal ideal of A; for such domains we show that every prime of A above a prime m containing I is maximal.
- Publication
Manuscripta Mathematica, 1990, Vol 67, Issue 1, p333
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF02568436