In this paper, we classify filiform associative algebras of degree p over a field of characteristic zero. Moreover, over an algebraically closed field of characteristic zero, we also classify filiform nilpotent associative algebras and naturally graded quasi-filiform nilpotent associative algebras, described through the characteristic sequence \(C({\mathcal {A}})=(n-2,1,1)\) or \(C({\mathcal {A}})=(n-2,2)\).

中文翻译：

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几类幂等联想代数

在本文中，我们将特征为零的场上度为p的丝状联想代数分类。此外，在特征为零的代数封闭域上，我们还通过特征序列\（C（{\ mathcal {A}}）=（n-2）描述了丝状幂幂联想代数和自然渐变的拟丝状幂幂联想代数。，1,1）\）或\（C（{\ mathcal {A}}）=（n-2,2）\）。