LAUSR

We identify minimal cases in which a power $$\mathfrak {m}^i\not =0$$mi≠0 of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring $$R/\mathfrak {m}^i$$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 $$\mathfrak {m}^4=0\ne \mathfrak {m}^3$$m4=0≠m3, the quotient $$R/\mathfrak {m}^3$$R/m3 is not Golod. This is provided that $$\mathfrak {m}$$m is minimally generated by at least 3 elements. Indeed, we show that if $$\mathfrak {m}$$m is 2-generated, then every power $$\mathfrak {m}^i\ne 0$$mi≠0 is Golod.