Separable algebras over infinite fields are 2-generated and finitely presented.
It is proved that a separable algebra over an infinite field \(K\) admits a finite presentation by two generators. This follows by the fact that the number of generators is invariant under field extension. As an application, the classification of two-dimensional simple \(K\langle x,y\rangle\)-modules [see \textit{H. Kraft}, in Representations of algebras, 3rd int. Conf., Puebla/Mex. 1980, Lect. Notes Math. 944, 180-258 (1982; Zbl 0517.14016)] is considered over a commutative ring.
scientific article; zbMATH DE number 5655337