A characterization of algebras generated by idempotents

We study algebras generated by idempotents. For finite dimensional algebras over a field, it turns out that these algebras can be characterized by their irreducible modules homologically. Particularly, we obtain that a finite dimensional algebra over an algebraically closed field is generated by ide...

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Veröffentlicht in:	Journal of pure and applied algebra 2021-09, Vol.225 (9), p.106693, Article 106693
Hauptverfasser:	Hu, Wei, Xiao, Zhankui
Format:	Artikel
Sprache:	eng
Schlagworte:	Idempotent Zero action determined module Zero product determined algebra
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Beschreibung
Zusammenfassung:	We study algebras generated by idempotents. For finite dimensional algebras over a field, it turns out that these algebras can be characterized by their irreducible modules homologically. Particularly, we obtain that a finite dimensional algebra over an algebraically closed field is generated by idempotents if and only if ExtA1(S,S)=0 for all 1-dimensional A-modules S.
ISSN:	0022-4049 1873-1376
DOI:	10.1016/j.jpaa.2021.106693