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arXiv · 1809.06105

Rank of elements of general rings in connection with unit-regularity

Nik Stopar
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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.

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Nik Stopar. 2018-09-17. Rank of elements of general rings in connection with unit-regularity. https://doi.org/10.1016/j.jpaa.2019.106211

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