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Finite local principal ideal rings (2301.07664v7)
Published 18 Jan 2023 in math.AC
Abstract: Every finite local principal ideal ring is the homomorphic image of a discrete valuation ring of a number field, and is determined by five invariants. We present an action of a group, non-commutative in general, on the set of Eisenstein polynomials, of degree matching the ramification index of the ring, over the coefficient ring. The action is defined by taking resultants.
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