7 citations · 11 across the 14 of their papers we have counts for
15 papers
On the projective dimension of tensor products of modules
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi
In this paper, we consider finitely generated modules over commutative Noetherian rings whose tensor products have finite projective dimension. We construct examples of modules of…
Finite Birational extension with stable conductor
Souvik Dey
Let be a module finite birational extension of a -dimensional local Cohen--Macaulay ring . When is the conductor of in a stable ideal? If is also generically…
Some characterizations of local rings via reducing dimensions
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +1
In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new character…
Trace ideal and annihilator of Ext and Tor of regular fractional ideals, and some applications
Souvik Dey
Given a commutative Noetherian ring with total ring of fractions , and a finitely generated -submodule of , we prove an equality between trace ideal, and cer…
Ulrich split rings
Hailong Dao, Souvik Dey, Monalisa Dutta
A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich modules split. In this paper we initiate the study of Ulrich split rings. We prove several…
On a generalized Auslander-Reiten conjecture
Souvik Dey, Shinya Kumashiro, Parangama Sarkar
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten con…
On the reducing projective dimension of the residue field
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +1
In this paper we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya-Celikbas and Araya-Takahashi…
Some new invariants of Noetherian local rings related to square of the maximal ideal
Dylan C. Beck, Souvik Dey
We introduce two new invariants of a Noetherian (standard graded) local ring that measure the number of generators of certain kinds of reductions of $\mathfrak m…
Vanishing of (co)homology of Burch and related submodules
Souvik Dey, Toshinori Kobayashi
We introduce the notion of Burch submodules and weakly -full submodules of modules over local rings and study their properties. One of our main results shows that Burc…
Complexity and rigidity of Ulrich modules, and some applications
Souvik Dey, Dipankar Ghosh
We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ul…
On the Subcategories of n-Torsionfree Modules and Related Modules
Souvik Dey, Ryo Takahashi
Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Br…
Comparisons between Annihilators of Tor and Ext
Souvik Dey, Ryo Takahashi
In this paper, we compare annihilators of Tor and Ext modules of finitely generated modules over a commutative noetherian ring. For local Cohen--Macaulay rings, one of our results…
Commutative rings with every non-maximal ideal finitely generated
Souvik Dey
In commutative ring theory, there is a theorem of Cohen which states that if in a commutative ring all prime ideals are finitely generated then every ideal is finitely generated. H…
Commutative rings over which the support of any module is the collection of prime ideals containing the annihilator
Souvik Dey
The support of any module over a commutative ring is defined as the collection of all prime ideals of the ring at which the localization of the module is non-zero. For finitely gen…
Classification of Rings which admits some special type of Polynomial functions
Souvik Dey
We know that for a finite field , every function on can be given by a polynomial with coefficients in . What about the converse? i.e. if is a ring (not necessarily co…