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 …

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 …

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 …

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 apply geometric techniques from representation theory to the study of homologically
finite differential graded (DG) modules M over a finite dimensional, positively graded …

Differential graded (DG) commutative algebra provides powerful techniques for proving
theorems about modules over commutative rings. These notes are a somewhat colloquial …

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 …

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 …

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 …

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 …