2021/06/30 by VandeBogert, Keller
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.00040
In this paper, we study conditions guaranteeing that a product of ideals defines a Golod ring. We show that for a 3-dimensional regular local ring (or 3-variable polynomial ring) (R , \m), the ideal I \m always defines a Golod ring for any proper ideal I ⊂ R. We also show that non-Golod products of ideals are ubiquitous; more precisely, we prove that for any proper ideal with grade ≥ 4, there exists an ideal J ⊆ I such that IJ is not Golod. We conclude by showing that if I is any proper ideal in a 3-dimensional regular local ring and \mfa ⊆ I a complete intersection, then \mfa I is Golod.