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 ${\mathrm{Ext}}_A^1(S,S)=0$ for all 1-dimensional A-modules S.

中文翻译：

---

由幂等生成的代数的刻画

我们研究由幂等产生的代数。对于一个域上的有限维代数，事实证明，这些代数可以用它们的不可约模块同质地表征。特别地，我们获得了当且仅当且仅当幂等生成代数闭合域上的有限维代数${\mathrm{分机}}_{\mathrm{一种}}^{\mathrm{1个}}（\mathrm{小号}，\mathrm{小号}）=0$为所有一维甲-模块小号。