Finite local principal ideal rings
Commutative Algebra
2025-04-03 v7
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.
Cite
@article{arxiv.2301.07664,
title = {Finite local principal ideal rings},
author = {Matthé van der Lee},
journal= {arXiv preprint arXiv:2301.07664},
year = {2025}
}
Comments
25 pages, 2 figures. Fixed a few typos. Clarified some of the arguments. Added a symbol index