2 citations · 2 across the 5 of their papers we have counts for
8 papers
Homological Detection by Perfectoid Algebras
Mohsen Asgharzadeh, Ryo Ishizuka
We first establish estimates for the projective and injective dimensions for quotients of perfectoid algebras by radical ideals. As applications, we obtain homological characteriza…
Perfect closure detects injective dimension
Mohsen Asgharzadeh
Let be a noetherian local ring of prime characteristic , and let denote its perfect closure. We prove that a finitely generated \(R\)-module has finite inject…
Non-Noetherian Bass and Betti numbers
Mohsen Asgharzadeh, Elham Mahdavi
This paper investigates the vanishing and non-vanishing of Betti and Bass numbers for non-finitely generated modules. We prove that for \(d\)-dimensional Cohen--Macaulay local ring…
A note on UFD
Mohsen Asgharzadeh
We investigate conditions under which height-one ideals are principal. As a representative case, let be a strongly normal, almost factorial, complete intersection local ring, a…
Finite support of tensor products
Mohsen Asgharzadeh
We determine the submodule of finite support of the tensor product of two modules M and N over a local ring and estimate its length in terms of and . Also, we compute higher…
On the initial Betti numbers
Mohsen Asgharzadeh
Let be a Cohen-Macaulay local ring possessing a canonical module. We compare the initial and terminal Betti numbers of modules in a series of nontrivial cases. We pay special a…