## Abstract

Let W be an associative PI-algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}G(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 id_{G}G(W)=id_{G}G(A^{*}) where A^{*} is the Grassmann envelope of A. 2. [. G-graded Specht problem] The T-ideal id_{G}G(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 id_{G}(W)=id_{G}(A).

Original language | English |
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Pages (from-to) | 2391-2428 |

Number of pages | 38 |

Journal | Advances in Mathematics |

Volume | 225 |

Issue number | 5 |

DOIs | |

State | Published - Dec 2010 |

Externally published | Yes |

## Keywords

- Graded algebra
- Polynomial identity