Publication Date:
2012-05-22
Description:
Given a finite group G and a field F of characteristic zero, we let F 〈 x 1, g 1 ,..., x r , g r 〉 be the free G -graded F -algebra generated by homogeneous variables { x i , g i } g i G . Let I be a G -graded T -ideal of F 〈 x 1, g 1 ,..., x r , g r 〉 which is PI (that is, the algebra F 〈 x 1, g 1 ,..., x r , g r 〉/I is PI). We prove that the Hilbert series of F 〈 x 1, g 1 ,..., x r , g r 〉/I is a rational function. More generally, we show that the Hilbert series which corresponds to any g -homogeneous component of F 〈 x 1, g 1 ,..., x r , g r 〉/I is a rational function.
Print ISSN:
0024-6093
Electronic ISSN:
1469-2120
Topics:
Mathematics
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