Let W be an associative PI-algebra over a field F of characteristic zero, graded by a finite group G. Let idGG(W) denote the T-ideal of G-graded identities of W. We prove: 1. [. G-graded PI-equivalence] There exists a field extension K of F and a finite-dimensional Z/2Z×G-graded algebra A over K such that idGG(W)=idGG(A*) where A* is the Grassmann envelope of A. 2. [. G-graded Specht problem] The T-ideal idGG(W) is finitely generated as a T-ideal. 3. [. G-graded PI-equivalence for affine algebras] Let W be a G-graded affine algebra over F. Then there exists a field extension K of F and a finite-dimensional algebra A over K such that idG(W)=idG(A).
- Graded algebra
- Polynomial identity