2014/10/02 by Trevor McGuire, McGuire, Trevor
Computer Science · Mathematics · #05E40 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1410.0713
openalex publication_date 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of free resolution algorithms have been given in both cases. In this present work, we will introduce similar techniques, or modify existing ones to obtain two new results. The first is S[Λ]-resolutions of Λ-invariant submodules of k[ℤn] where Λ is a lattice in ℤn satisfying some trivial conditions. A consequence will be the ability to resolve submodules of k[ℤn/Λ], and in particular ideals J of S/IΛ, where IΛ is the lattice ideal of Λ. Second, we will provide a detailed account in three dimensions on how to lift the aforementioned resolutions to resolutions in k[x,y,z] of ideals with monomial and binomial generators.