Perfect ideals of grade 3 can be classified based on algebra structures on their minimal free
resolutions. The classification is incomplete in the sense that it remains open which of the …

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) …

Abstract Let (R, m, k) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R
of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd …

Alexis Hardesty Page 1 Alexis Hardesty Webpage: math.ttu.edu/alexigom/ Research Statement
Email: alexis.hardesty@ttu.edu For many scientific disciplines, mathematics provides a …

Ideals in the algebra of power series in three variables can be classified based on algebra
structures on their minimal free resolutions. The classification is incomplete in that it remains …