PRODUCTS OF IDEALS AND GOLOD RINGS

Authors

• Keller Vandebogert, University of KentuckyFollow

Abstract

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) (R, m), the ideal Im always defines a Golod ring for any proper ideal I ⊂ R. We also show that non-Golod products of ideals are ubiquitous; more precisely, we prove that for any proper ideal with grade ≥ 4, there exists an ideal J ⊆ I such that IJ is not Golod. We conclude by showing that if I is any proper ideal in a 3-dimensional regular local ring and a ⊆ I a complete intersection, then aI is Golod.

Document Type

Article

Publication Date

8-1-2022

Notes/Citation Information

Publisher Copyright: © 2022 American Mathematical Society.

Digital Object Identifier (DOI)

10.1090/proc/15968

Archival?

Archival

Repository Citation

Vandebogert, Keller, "PRODUCTS OF IDEALS AND GOLOD RINGS" (2022). Mathematics Faculty Publications. 74.
https://uknowledge.uky.edu/math_facpub/74