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Polynomials inducing the zero function on chain rings

    We provide a minimal set of generators for the ideal of polynomials in R[x] that map the maximal ideal 𝔪 into one of its powers 𝔪n, where (R,𝔪) is a discrete valuation ring with a finite residue field. We use this to provide a minimal set of generators for the ideal of polynomials in R[x] that send 𝔪 to zero, where (R,𝔪) is a finite commutative local principal ideal ring.

    Communicated by R. Wiegand

    AMSC: 13M10, 13B25, 11C08, 13J15, 13E10, 13F20, 13E15, 13F10

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