In this paper, we study conditions guaranteeing that a product of ideals defines a Golod ring.
We show that for a $3 $-dimensional regular local ring (or $3 $-variable polynomial ring) …

On Monomial Golod Ideals | Acta Mathematica Vietnamica Skip to main content SpringerLink
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Let S be a regular local ring or a polynomial ring over a field and I be an ideal of S.
Motivated by a recent result of Herzog and Huneke, we study the natural question of whether …

We exhibit an example of a product of two proper monomial ideals such that the residue
class ring is not Golod. We also discuss the strongly Golod property for rational powers of …

We prove that the integral closure of a strongly Golod ideal in a polynomial ring over a field
of characteristic zero is strongly Golod, positively answering a question of Huneke. More …

We identify minimal cases in which a power m^ i\not= 0 mi≠ 0 of the maximal ideal of a local
ring R is not Golod, ie the quotient ring R/m^ i R/mi is not Golod. Complementary to a 2014 …

Let A= K [x1,..., xn] be a polynomial ring over a fieldK, and let R= A/I be the quotient of A by
an ideal I⊂ A that is homogeneous with respect to the standard grading in which deg (xi)= 1 …

Let S be a positively graded polynomial ring over a field of characteristic 0, and I⊂ S a
proper graded ideal. In this note it is shown that S/I is Golod if∂(I) 2⊂ I. Here∂(I) denotes …

Let S= 𝕂 [x₁,..., xn] be the polynomial ring over a field 𝕂 In this paper we present a criterion
for componentwise linearity of powers of monomial ideals. In particular, we prove that if a …

Ideals Defining Gorenstein Rings Are (Almost) Never Products Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 135, Number 7, July 2007, Pages 2003-2005 …