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

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Abstract

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.

Original languageEnglish
Pages (from-to)549-562
Number of pages14
JournalArchiv der Mathematik
Volume110
Issue number6
DOIs
StatePublished - Jun 1 2018

Keywords

  • Artinian Gorenstein ring
  • Exact zero-divisor
  • Golod ring
  • Koszul ring

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