TY - JOUR
T1 - The Golod property of powers of the maximal ideal of a local ring
AU - Christensen, Lars Winther
AU - Veliche, Oana
N1 - Funding Information:
L.W.C. was partly supported by NSA Grant H98230-14-0140 and Simons Foundation collaboration Grant 428308.
Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We identify minimal cases in which a power mi≠ 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 ≠ 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≠ 0 is Golod.
AB - We identify minimal cases in which a power mi≠ 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 ≠ 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≠ 0 is Golod.
KW - Artinian Gorenstein ring
KW - Exact zero-divisor
KW - Golod ring
KW - Koszul ring
UR - http://www.scopus.com/inward/record.url?scp=85044953532&partnerID=8YFLogxK
U2 - 10.1007/s00013-018-1152-6
DO - 10.1007/s00013-018-1152-6
M3 - Article
AN - SCOPUS:85044953532
SN - 0003-889X
VL - 110
SP - 549
EP - 562
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 6
ER -