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Polynômes à valeurs entières sur un anneau non analytiquement irréductible. Integer valued polynomials over a non analytically irreducible ring). (French) Zbl 0722.13005
We let A be a noetherian onedimensional local domain, K its field of fractions, \({\mathfrak m}\) its maximal ideal; we suppose that its integral closure \(A'\) is an A-module of finite type but is not local (hence A is not analytically irreducible). We show that the prime ideals above \({\mathfrak m}\) of the ring of integer valued polynomials \(A[X]_{sub}=\{P\in K[X]| P(A)\subset A\}\) are finitely many and give a complete description in the case where K is a quadratic extension of \({\mathbb{Q}}\).

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13A15 Ideals and multiplicative ideal theory in commutative rings
13B25 Polynomials over commutative rings
13H99 Local rings and semilocal rings
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