Tight closure of ideals on Witt rings

TL;DR

This paper introduces the concept of tight closure of ideals on Witt rings, explores quasi-$F$-rationality, and examines the relationship between closure operators and integral closure, advancing understanding in algebraic structures.

Contribution

It defines tight closure on Witt rings and characterizes quasi-$F$-rationality, providing new insights into closure operations and their algebraic implications.

Findings

Characterization of quasi-$F$-rationality

Relationship between closure operator and integral closure

Introduction of tight closure notions on Witt rings

Abstract

In this paper, we introduce the notions of tight closure of ideals on Witt rings and quasi-tightly closedness of system of parameters. By using the notions, we obtain a characterization of quasi-$F$-rationality. Furthermore, we study the relationship between the closure operator and integrally closure.