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Type: | Artigo |

Title: | A Note On Graded Polynomial Identities For Tensor Products By The Grassmann Algebra In Positive Characteristic |

Author: | Centrone Lucio; Tomaz da Silva Viviane Ribeiro |

Abstract: | Let G be a finite abelian group. As a consequence of the results of Di Vincenzo and Nardozza, we have that the generators of the T-G-ideal of G-graded identities of a G-graded algebra in characteristic 0 and the generators of the T-GxZ2 -ideal of G x Z(2)-graded identities of its tensor product by the infinite-dimensional Grassmann algebra E endowed with the canonical grading have pairly the same degree. In this paper, we deal with Z(2) x Z(2)-graded identities of E-k* circle times E over an infinite field of characteristic p > 2, where E-k* is E endowed with a specific Z(2)-grading. We find identities of degree p + 1 and p + 2 while the maximal degree of a generator of the Z(2)-graded identities of E-k* is p if p > k. Moreover, we find a basis of the Z(2) x Z(2)-graded identities of E-k (*) circle times E and also a basis of multihomogeneous polynomials for the relatively free algebra. Finally, we compute the Z(2) x Z(2)-graded Gelfand-Kirillov (GK) dimension of E-k* circle times E. |

Subject: | Graded Identities Grassmann Algebra |

Editor: | World Scientific Publ CO PTE LTD Singapore |

Rights: | fechado |

Identifier DOI: | 10.1142/S0218196716500478 |

Address: | http://www-worldscientific-com.ez88.periodicos.capes.gov.br/doi/abs/10.1142/S0218196716500478 |

Date Issue: | 2016 |

Appears in Collections: | Unicamp - Artigos e Outros Documentos |

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000383987200001.pdf | 236.2 kB | Adobe PDF | View/Open |

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