6 papers · 1 filter
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…
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…
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…
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…