2000 character limit reached
Group graded PI-algebras and their codimension growth
Published 6 Feb 2010 in math.RA | (1002.1385v1)
Abstract: Let W be an associative PI-algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote the codimension growth of W and of the identity component W_e, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W)\leq |G|2 exp(W_e). The inequality is known in case the algebra W is affine (i.e. finitely generated). Here we prove the conjecture in general.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.