2 citations · 3 across the 9 of their papers we have counts for
11 papers · 1 filter
Quasi-Gorenstein (Normal) Finite Covers in Arbitrary Characteristic
Ehsan Tavanfar
We show that any complete local (normal) domain admits a module-finite quasi-Gorenstein normal (complete local) domain extension. In the geometric vein, we show that any normal pro…
Remarks on the Small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules
Kazuma Shimomoto, Ehsan Tavanfar
We show that any quasi-Gorenstein deformation of a -dimensional quasi-Gorenstein Buchsbaum local ring with -invariant admits a maximal Cohen-Macaulay module, provided it…
Reductions towards a characteristic free proof of the Canonical Element Theorem
Ehsan Tavanfar
We reduce Hochster's Canonical Element Conjecture (theorem since 2016) to a localization problem in a characteristic free way. We prove the validity of a new variant of the Canonic…
On local rings without small Cohen-Macaulay algebras in mixed characteristic
Kazuma Shimomoto, Ehsan Tavanfar
For any , by deformation theory of schemes, we present examples of (complete or excellent) -dimensional mixed characteristic normal local domains admitting no small Cohe…
Test modules, weakly regular homomorphisms and complete intersection dimension
Ehsan Tavanfar
We prove that if a local ring admits a (pd-)test module of finite complete intersection dimension, then it is a complete intersection ring. This answers, positively, a question pro…
A Study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property
Kazuma Shimomoto, Naoki Taniguchi, Ehsan Tavanfar
In the present article, we investigate the following deformation problem. Let be a local (graded local) Noetherian ring with a (homogeneous) regular element $y \i…
Annihilators of Koszul Homologies and Almost Complete Intersections
Ehsan Tavanfar
In this article, we propose a question on the annihilators of positive Koszul homologies of a system of parameters of an almost complete intersection . The question can be state…
Reduction of some homological conjectures to excellent unique factorization domains
Ehsan Tavanfar
In this article, applying the quasi-Gorenstein analogous of the Ulrich's deformation of certain Gorenstein rings we show that some homological conjectures, including the Monomial C…
A Study of Quasi-Gorenstein Rings
Ehsan Tavanfar, Massoud Tousi
In this paper several quasi-Gorenstein counterparts to some known properties of Gorenstein rings are given. We, furthermore, give an explicit description of the attach prime ideals…
On the New Intersection Theorem for totally reflexive modules
Kamran Divaani-Aazar, Fatemeh Mohammadi Aghjeh Mashhad, Ehsan Tavanfar +1
Let (R,m,k) be a local ring. We establish a totally reflexive analogue of the New Intersection Theorem, provided for every totally reflexive R-module M, there is a big Cohen-Macaul…
On the Graded Annihilators of Right Modules Over The Frobenius Skew Polynomial Ring
Ehsan Tavanfar
Let R be a commutative Noetherian ring of prime characteristic and M be an x-divisible right R[x,f]-module that is Noetherian as R-module. We give an affirmative answer to the ques…