4 papers
Cohomological Cohen--Macaulayness in Non-Noetherian Rings
Ryoya Ando
We study Cohen--Macaulayness, in the sense of Hamilton--Marley, of non-Noetherian rings arising as big Cohen--Macaulay algebras. Motivated by Bhatt's notion of cohomological Cohen-…
Polynomial Extensions and Localization of Non-Noetherian Cohen--Macaulay Rings
Ryoya Ando
This paper studies polynomial extensions and localization of HMCM rings, where HMCM means Cohen--Macaulay in the sense of Hamilton--Marley, a notion for non-Noetherian rings. We sh…
On torsion-free modules and semi-hereditary rings
Ryoya Ando
The class of semi-hereditary rings is an important class of rings in theories that do not assume the Noetherian condition, such as perfectoid ring theory. We prove several results…
A note on weakly proregular sequences and local cohomology
Ryoya Ando
In this note, we give an elementary proof of the result given by Schenzel that there are functorial isomorphisms between local cohomology groups and Čech cohomology groups, by usin…