ИСТИНА

Kemer proved that every affine algebra over an infinite field F is PI-equivalent to a finite dimensional algebra. In order to extend this result to finite fields F, one must introduce the concept of Zariski closed algebras. These are a useful generalization of finite dimensional algebras,to which many of the important structure theorems of finite dimensional algebras can be generalized, including Wedderburn's Principal Theorem for example, they are a key ingredient in Belov's proof of Specht's conjecture for affine algebras over an arbitrary field.