Cohen-Macaulay approximations and the SC_r-condition

2025/07/19 by Bartels, Richard F.
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.14424

Abstract

We study the relation between MCM approximations and FID hulls of modules over a Cohen-Macaulay local ring R with canonical module, specifically when R is generically Gorenstein. We then generalize a result of Kato, who proved that a Gorenstein complete local ring R satisfies the SC₂-condition if and only if R is a UFD. For r ≥ 3, we prove a criterion for when an MCM R-module M satisfies the SC_r-condition, assuming that its first syzygy Ω_R¹(M) satisfies the SC_r-1-condition.

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