Cleanness of a Dubrovin valuation ring

An order R in a simple Artinian ring Q is said to be a Dubrovin valuation ring if R is Bezout and R/J(R) is a simple Artinian, where J(R) is the Jacobson radical of R. A ring R with unity is called clean, if every element x ∈ R is clean i.e. for every element x ∈ R there exist an idempotent element...

Full description

Saved in:
Bibliographic Details
Main Authors: Ambarsari, Ida Fitriana, Irawati, Santi, Sulandra, I. Made, Susanto, Hery, Marubayashi, Hidetoshi
Format: Conference Proceeding
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An order R in a simple Artinian ring Q is said to be a Dubrovin valuation ring if R is Bezout and R/J(R) is a simple Artinian, where J(R) is the Jacobson radical of R. A ring R with unity is called clean, if every element x ∈ R is clean i.e. for every element x ∈ R there exist an idempotent element e ∈ R and a unit element u ∈ R such that x=e+u. In this article, it will be investigated some properties of clean Dubrovin valuation ring and give some examples related to a Dubrovin valuation ring and a clean ring.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5139127