Abstract
Let R[X] be a polynomial ring in one variable over a commutative ring R. If (R,ℳ) is a local ring then any Weierstrass polynomial in R[X] is contained only in the maximal ideal (ℳ,X) of R[X]. We generalise this property of Weierstrass polynomials and investigate properties of polynomials contained in a finite number of maximal ideals in R[X].
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