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

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

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...

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Veröffentlicht in:Journal of pure and applied algebra 2020-04, Vol.224 (4), p.106211, Article 106211
1. Verfasser: Stopar, Nik
Format: Artikel
Sprache:eng
Schlagworte:
Idempotent
Minimal right ideal
Rank
Unit-regular element
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Beschreibung
Zusammenfassung: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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2019.106211