| Texto completo | |
| Autor(es): |
Centrone, Lucio
;
Tomaz da Silva, Viviane Ribeiro
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 26, n. 6, p. 1125-1140, SEP 2016. |
| Citações Web of Science: | 0 |
| Resumo | |
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. (AU) | |
| Processo FAPESP: | 15/08961-5 - Crescimento de álgebras com identidades polinomiais |
| Beneficiário: | Lucio Centrone |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 13/06752-4 - Cocaracteres e dimenção de Gelfand-Kirillov de PI-álgebras |
| Beneficiário: | Lucio Centrone |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |