Rank of elements of general rings in connection with unit-regularity
Rings and Algebras
2023-08-28 v1
Abstract
We define the rank of elements of general unital rings, discuss its properties and give several examples to support the definition. In semiprime rings we give a characterization of rank in terms of invertible elements. As an application we prove that every element in the socle of a unital semiprime ring is unit-regular.
Cite
@article{arxiv.1809.06105,
title = {Rank of elements of general rings in connection with unit-regularity},
author = {Nik Stopar},
journal= {arXiv preprint arXiv:1809.06105},
year = {2023}
}
Comments
13 pages