[HTML][HTML] Applications and homological properties of local rings with decomposable maximal ideals
We construct a local Cohen–Macaulay ring R with a prime ideal p∈ Spec (R) such that R
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …
Relative Tor functors with respect to a semidualizing module
Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
Presentations of rings with non-trivial semidualizing modules
DA Jorgensen, GJ Leuschke… - Collectanea mathematica, 2012 - Springer
Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
On reducing homological dimensions over noetherian rings
T Araya, R Takahashi - Proceedings of the American Mathematical Society, 2022 - ams.org
Let $\Lambda $ be a left and right Noetherian ring. First, for $ m, n\in\mathbb {N}\cup\{\infty\}
$, we give equivalent conditions for a given $\Lambda $-module to be $ n $-torsionfree and …
$, we give equivalent conditions for a given $\Lambda $-module to be $ n $-torsionfree and …
Geometric aspects of representation theory for DG algebras: answering a question of Vasconcelos
S Nasseh, S Sather‐Wagstaff - Journal of the London …, 2017 - Wiley Online Library
We apply geometric techniques from representation theory to the study of homologically
finite differential graded (DG) modules M over a finite dimensional, positively graded …
finite differential graded (DG) modules M over a finite dimensional, positively graded …
A somewhat gentle introduction to differential graded commutative algebra
KA Beck, S Sather-Wagstaff - Connections Between Algebra …, 2014 - Springer
Differential graded (DG) commutative algebra provides powerful techniques for proving
theorems about modules over commutative rings. These notes are a somewhat colloquial …
theorems about modules over commutative rings. These notes are a somewhat colloquial …
Ring homomorphisms and local rings with quasi-decomposable maximal ideal
S Nasseh, KA Sather-Wagstaff… - Communications in …, 2024 - Taylor & Francis
The notion of local rings with quasi-decomposable maximal ideal was formally introduced by
Nasseh and Takahashi. In separate works, the authors of the present paper showed that …
Nasseh and Takahashi. In separate works, the authors of the present paper showed that …
Generic constructions and semidualizing modules
SK Sather-Wagstaff, T Se, S Spiroff - Algebras and Representation Theory, 2021 - Springer
Generic Constructions and Semidualizing Modules Page 1 Algebras and Representation Theory
(2021) 24:1071–1081 https://doi.org/10.1007/s10468-020-09979-5 Generic Constructions and …
(2021) 24:1071–1081 https://doi.org/10.1007/s10468-020-09979-5 Generic Constructions and …
On semidualizing modules of ladder determinantal rings
S Sather-Wagstaff, T Se, S Spiroff - 2019 - projecteuclid.org
We identify all semidualizing modules over certain classes of ladder determinantal rings
over a field k. Specifically, given a ladder of variables Y, we show that the ring k [Y]/I t (Y) has …
over a field k. Specifically, given a ladder of variables Y, we show that the ring k [Y]/I t (Y) has …
Lower bounds for the number of semidualizing complexes over a local ring
S Sather-Wagstaff - Mathematica Scandinavica, 2012 - JSTOR
We investigate the set 𝔖 (R) of shift-isomorphism classes of semi-dualizing R-complexes,
ordered via the reflexivity relation, where R is a commutative noetherian local ring …
ordered via the reflexivity relation, where R is a commutative noetherian local ring …