Finite local principal ideal rings

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.

25 pages, 2 figures. Fixed a few typos. Clarified some of the arguments. Added a symbol index