Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Golod property of powers of the maximal ideal of a local ring   We identify minimal cases in which a power $m^i\not=0$ of the maximal ideal
of a local ring $R$ is not Golod, i.e.\ the quotient ring $R/m^i$ is not Golod.
Complementary to a 2014 result by Rossi and \c{S}ega, we prove that for a
generic artinian Gorenstein local ring with $m^4=0\not= m^3$, the quotient
$R/m^3$ 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 $m^i\not= 0$ is Golod.

4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an