4 papers
Matijevic-Roberts type theorems, Rees rings and associated graded rings
Jun Horiuchi, Kazuma Shimomoto
The aim of this article is to investigate interrelated structures lying among three notable problems in commutative algebra. These are Lifting problem, Ascent/descent along associa…
Some ring-theoretic properties of rings via Frobenius and monoidal maps
Kazufumi Eto, Jun Horiuchi, Kazuma Shimomoto
The purpose of this note is to relate certain ring-theoretic properties of rings in mixed and positive characteristics that are related to each other by a tilting operation used in…
Weak normality and seminormality in the mixed characteristic case
Jun Horiuchi, Kazuma Shimomoto
In this article, we give a few examples of local rings in relation to weak normality and seminormality in mixed characteristic. It is known that two concepts can differ in the equa…
Normal hyperplane sections of normal schemes in mixed characteristic
Jun Horiuchi, Kazuma Shimomoto
The aim of this article is to prove that, under certain conditions, an affine flat normal scheme that is of finite type over a local Dedekind scheme in mixed characteristic admits…