Koszul cycles and Golod rings

2017/01/24 by Jürgen Herzog, Herzog, Jürgen, Rasoul Ahangari Maleki +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1701.06738

openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be the power series ring or the polynomial ring over a field K in the variables x₁,…,x_n, and let R=S/I, where I is proper ideal which we assume to be graded if S is the polynomial ring. We give an explicit description of the cycles of the Koszul complex whose homology classes generate the Koszul homology of R=S/I with respect to x₁,…,x_n. The description is given in terms of the data of the free S-resolution of R. The result is used to determine classes of Golod ideals, among them proper ordinary powers and proper symbolic powers of monomial ideals. Our theory is also applied to stretched local rings.

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