The Golod property of powers of the maximal ideal of a local ring

摘要

We identify minimal cases in which a power of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring is not Golod. Complementary to a 2014 result by Rossi and Aega, we prove that for a generic artinian Gorenstein local ring with , the quotient is not Golod. This is provided that is minimally generated by at least 3 elements. Indeed, we show that if is 2-generated, then every power is Golod.