Products of ideals may not be Golod
Alessandro De Stefani
TL;DR
This paper provides a counterexample showing that the product of two monomial ideals need not produce a Golod ring, and explores properties related to Golodness in monomial ideals and their powers.
Contribution
It introduces a specific example of non-Golod product of monomial ideals and discusses conditions for Golodness and weak Golodness in monomial ideals and their rational powers.
Findings
Counterexample of non-Golod product of monomial ideals
Conditions for weak Golodness of monomial ideals
Analysis of strongly Golod property in rational powers
Abstract
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 monomial ideals, and introduce some sufficient conditions for weak Golodness of monomial ideals. Along the way, we ask some related questions.
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