Filtered Ring Derived from Discrete Valuation Ring and Its Properties

TL;DR

This paper demonstrates that discrete valuation rings are examples of filtered rings and explores their properties and relationships within this framework.

Contribution

It establishes that discrete valuation rings are filtered rings and investigates their properties and interrelations.

Findings

Discrete valuation rings are filtered rings.

Several properties of these filtered rings are characterized.

Relations between discrete valuation rings and filtered ring structures are analyzed.

Abstract

In this paper we show that if R is a discrete valuation ring, then R is a filtered ring. We prove some properties and relation when R is a discrete valuation ring.