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

被引：3

作者：

Christensen, Lars Winther ^{[1
]}

Veliche, Oana ^{[2
]}

机构：

[1] Texas Tech Univ, Lubbock, TX 79409 USA

[2] Northeastern Univ, Boston, MA 02115 USA

来源：

ARCHIV DER MATHEMATIK | 2018年 / 110卷 / 06期

关键词：

Artinian Gorenstein ring; Exact zero-divisor; Golod ring; Koszul ring; POINCARE-SERIES; FREE RESOLUTIONS; GORENSTEIN RING; MODULES; ALGEBRAS; SOCLE;

D O I：

10.1007/s00013-018-1152-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：549 / 562

页数：14

共 23 条

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