Rings in Which Element is a Sum of the Transformation Elements of Idempotents and Special Elements
Year: 2025
Type: article
Abstract: In this article, further generalizations are made for the nil clean ring and the ur‐clean ring, obtained as extensions of the clean ring. Firstly, consider rings where each element can be expressed as n idempotents plus one nilpotent, any two commute under multiplication. Some properties of this ring and its relationship to some special rings will be discussed in this paper. Secondly, replace the idempotent element that make up the ur‐clean ring with the quasi‐idempotent element to obtain ur‐quasi‐clean ring. Finally, the ur‐quasi‐cleanness will be considered on the involution rings, define by ∗ ur‐quasi‐clean rings.
Source: Journal of Mathematics
DOI: 10.1155/jom/5699805
Authors: Xinsong Yang, Jiaxin Liu
Institution: Harbin University of Science and Technology
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W4411747378