2017/01/23 by H. Ananthnarayan, Ananthnarayan, H., Rajiv Kumar +1
Mathematics · #13C14 #13D02 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A02
paper · pdf · doi:10.48550/arxiv.1701.06475
openalex publication_date 2017/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in terms of graded Betti numbers, called the Herzog-Kuhl equations, for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) - depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing all graded Cohen-Macaulay R-modules.