Decompositions of Cellular Binomial Ideals

Abstract

Without any restrictions on the base field, we compute the hull and prove a conjecture of Eisenbud and Sturmfels giving an unmixed decomposition of a cellular binomial ideal. Over an algebraically closed field, we further obtain an explicit (but not necessarily minimal) primary decomposition of such an ideal.

Improved proofs of Corollary 3.7, Proposition 3.9, Theorem 4.1 and Theorem 4.3

References in corpus (2)

• Decompositions of commutative monoid congruences and binomial ideals
• Decompositions of Binomial Ideals in Macaulay 2

Cited by in corpus (2)

• Binomial ideals and congruences on ${\mathbb{N}}^n$
• Some algebraic aspects of mesoprimary decomposition