1 citations · 1 across the 6 of their papers we have counts for
12 papers
Frobenius multiplicities and F-signatures of Grassmannians of two-planes
Justin Lyle
Raedschelders, Špenko and Van den Bergh proved that the Plücker coordinate ring of the Grassmannian has finite Frobenius representation type when the…
On the totally acyclic condition and the Auslander-Reiten Conjecture
Justin Lyle
We prove new cases of the Auslander-Reiten conjecture under the assumption that the base ring satisfies the totally acyclic condition . A consequence of our work is…
A counterexample to the localization problem for AB rings
Justin Lyle, Saeed Nasseh
We construct a complete local Gorenstein ring of dimension with a prime ideal such that is an AB ring, but the localization $R_…
On the vanishing of Ext modules over a local unique factorization domain with an isolated singularity
Kaito Kimura, Justin Lyle, Yuya Otake +1
This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preservin…
On a generalization of Ulrich modules and its applications
Ela Celikbas, Olgur Celikbas, Justin Lyle +2
We study a modified version of the classical Ulrich modules, which we call -Ulrich. Unlike the traditional setting, -Ulrich modules always exist. We prove that these modules…
Exterior powers and Tor-persistence
Justin Lyle, Jonathan Montaño, Keri Sather-Wagstaff
A commutative Noetherian ring is said to be Tor-persistent if, for any finitely generated -module , the vanishing of for implies $M…
Minimal Cohen-Macaulay Simplicial Complexes
Hailong Dao, Joseph Doolittle, Justin Lyle
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give suff…
Extremal growth of Betti numbers and trivial vanishing of (co)homology
Justin Lyle, Jonathan Montaño
A Cohen-Macaulay local ring satisfies trivial vanishing if for all large implies or has finite projective dimension. If satisfie…
Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
Toshinori Kobayashi, Justin Lyle, Ryo Takahashi
We say that a Cohen-Macaulay local ring has finite -representation type if there exist only finitely many isomorphism classes of indecomposable maxima…
Rank Selection and Depth Conditions for Balanced Simplicial Complexes
Brent Holmes, Justin Lyle
We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that rank selected subcomplexes of balanced simplicial complexes satisfying Serr…
Hom and Ext, Revisited
Hailong Dao, Mohammad Eghbali, Justin Lyle
Let be a commutative Noetherian local ring and be finitely generated -modules. We prove a number of results of the form: if $\mbox{Hom}_R(M,N)$ has some nice propertie…
Higher Nerves of Simplicial Complexes
Hailong Dao, Joseph Doolittle, Ken Duna +3
We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of t…