English

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.

Keywords

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}
}

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13 pages