2010/06/29 by Max Joachim Nitsche, Nitsche, Max Joachim
Computer Science · Mathematics · #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1006.5670
openalex publication_date 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a field, B a simplicial affine semigroup, and C(B) the corresponding cone. We will present a decomposition of K[B] into a direct sum of certain monomial ideals, which generalizes a construction by Hoa and Stückrad. We will use this decomposition to construct a semigroup B with B ⊆ B ⊆ C(B) such that K[ B] is Cohen-Macaulay with the property: B ⊆ B for every affine semigroup B with B ⊆ B ⊆ C(B) such that K[ B] is Cohen-Macaulay.