Rank of elements of general rings in connection with unit-regularity
arXiv:1809.06105 · doi:10.1016/j.jpaa.2019.106211
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.
13 pages