Quasi valuation and valuation derived from filtered ring and properties

TL;DR

This paper introduces methods to define quasi valuations and valuations on filtered rings, exploring their properties and relationships to enhance understanding of algebraic structures.

Contribution

It presents new ways to derive valuations from filtered rings and establishes foundational properties and relations for these valuations.

Findings

Defined quasi valuations on filtered rings

Established conditions for valuations on filtered rings

Proved properties and relations of these valuations

Abstract

In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.