@inproceedings{58370d9fd91f438dab80248e2fae7d24,
title = "The relationships between clean rings, r-clean rings, and f-clean rings",
abstract = "Suppose R is a ring with identity. R called a regular ring if each element is a regular element. A ring R is called an r-clean ring if every element in R can be expressed as the sum of a regular element and an idempotent element. An element in the ring R is called clean if it can be expressed as the sum of a unit element and an idempotent element, so the ring R is called a clean ring if every element is clean. A ring of which each element is a full element is called an f-clean ring. We give some relationships between clean rings, regular rings, r-clean rings, and f-clean rings.",
keywords = "Clean rings, commutative ring, element",
author = "Ari Andari",
note = "Publisher Copyright: {\textcopyright} 2018 Author(s).; 8th Annual Basic Science International Conference: Coverage of Basic Sciences toward the World's Sustainability Challanges, BaSIC 2018 ; Conference date: 06-03-2018 Through 07-03-2018",
year = "2018",
month = oct,
day = "17",
doi = "10.1063/1.5062768",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Corina Karim and Rodliyati Azrianingsih and Pamungkas, \{Mauludi Ariesto\} and Jatmiko, \{Yoga Dwi\} and Anna Safitri",
booktitle = "8th Annual Basic Science International Conference",
}