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Remarks on some Homological Problems regarding Infinite Integral Extensions
Mohsen Asgharzadeh, Shravan Patankar
Let be an excellent local domain. is said to be if for some . Bhatt, Iyengar, and Ma ask if equi-characteristic zero $N…
Remarks on modules of finite projective dimension
Mohsen Asgharzadeh, Elham Mahdavi
We investigate homological and depth-theoretic properties of finitely generated modules of finite projective dimension over Noetherian local rings. A central theme is the study of…
Annihilator of
Mohsen Asgharzadeh
We investigate the higher divisorial ideal associated to an ideal of grade . Our main focus is the containment problem $ D(I) \subseteq \overli…
Integral closure of 1-dimensional rings
Mohsen Asgharzadeh
We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity…
Vector space summands of lower syzygies
Mohsen Asgharzadeh, Michael DeBellevue, Souvik Dey +2
In this paper, we investigate problems concerning when the residue field of a local ring , appears as a direct summand of syzygy modules, from two perspectives…
Homology of conductor
Mohsen Asgharzadeh
We study some homological properties of the conductor ideal.
A note on cohomological vanishing theorems
Mohsen Asgharzadeh
We study , and we prove the following over -rings: iff . For locally free over the punctured spectru…
Notes on modules of finite injective dimension
Mohsen Asgharzadeh
Motivated by Bass' conjecture, we study finitely generated modules of finite injective dimension and the additional constraints they impose on the ambient ring. Beyond ensuring the…