7 papers · 1 filter
Trace ideals of syzygies
Haydee Lindo, Justin Lyle, Sarasij Maitra
We study the behavior of trace ideals under taking syzygies. In particular, when is numerical semigroup ring and is a homogeneous ideal in , we obtain an upper estimate…
Centers of Endomorphism Rings and Reflexivity
Souvik Dey, Justin Lyle
Let be a local ring and let be a finitely generated -module. Appealing to the natural left module structure of over its endomorphism ring and corresponding center $Z…
Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goa…
On the depth of tensor products over Cohen-Macaulay rings
Kaito Kimura, Justin Lyle, Andrew J. Soto-Levins
Inspired by classical work on the depth formula for tensor products of finitely generated -modules, we introduce two conditions which we call and $(\mathbf{rde…
Annihilators of (co)homology and their influence on the trace Ideal
Justin Lyle, Sarasij Maitra
Let be a commutative Noetherian local ring, and suppose is Cohen-Macaulay with canonical module . We develop new tools for analyzing questions involving…
Generalized trace submodules and centers of endomorphism rings
Justin Lyle
Let be a commutative Noetherian local ring and a finitely generated -module. We introduce a general form of the classically studied trace map that unifies several notion…
Endomorphism algebras over commutative rings and torsion in self tensor products
Justin Lyle
Let be a commutative Noetherian local ring. We study tensor products involving a finitely generated -module through the natural action of its endomorphism ring. In parti…