2017/08/09 by Christensen, Lars Winther, Veliche, Oana
#13D02 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.02815
We identify minimal cases in which a power mi\not=0 of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring R/mi is not Golod. Complementary to a 2014 result by Rossi and Şega, we prove that for a generic artinian Gorenstein local ring with m4=0\not= m3, the quotient R/m3 is not Golod. This is provided that m is minimally generated by at least 3 elements. Indeed, we show that if m is 2-generated, then every power mi\not= 0 is Golod.