Irreducible decomposition of binomial ideals
Commutative Algebra
2019-02-20 v2 Combinatorics
Abstract
Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct decompositions that are direct combinatorial analogues of binomial irreducible decompositions, and for binomial ideals we construct decompositions into ideals that are as irreducible as possible while remaining binomial. We provide an example of a binomial ideal that is not an intersection of binomial irreducible ideals, thus answering a question of Eisenbud and Sturmfels [1996].
Cite
@article{arxiv.1503.02607,
title = {Irreducible decomposition of binomial ideals},
author = {Thomas Kahle and Ezra Miller and Christopher O'Neill},
journal= {arXiv preprint arXiv:1503.02607},
year = {2019}
}
Comments
15 pages, 3 figures, v2: minor changes implemented during copy-editing, final version as in Compositio Mathematica