Irreducible decomposition of binomial ideals

Thomas Kahle, Ezra Miller, Christopher O'Neill
2016 Compositio Mathematica  
Building on coprincipal mesoprimary decomposition [Kahle and Miller,Decompositions of commutative monoid congruences and binomial ideals, Algebra and Number Theory8(2014), 1297–1364], 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
more » ... ompositions 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 irreducible binomial ideals, thus answering a question of Eisenbud and Sturmfels [Binomial ideals, Duke Math. J.84(1996), 1–45].
doi:10.1112/s0010437x16007272 fatcat:rqyanhl7ojhbvgor4wrmchbmla