Algebraic Properties of Codimension Series of PI-Algebras

Details Algebraic Properties of Codimension Series of PI-Algebras Algebraic Properties of Codimension Series of PI-Algebras

2011-11-01

arxiv.org/abs/1111.0319v1

Mathematics

Rings and Algebras

14 pages

Scientific paper

For a PI-algebra R over a field of characteristic 0 let T(R) be the T-ideal of the polynomial identities of R and let c(R,t) be the codimension series of R (i.e., the generating function of the codimension sequence of R). Let A, B and R be PI-algebras such that T(R)=T(A)T(B). We show that if c(A,t) and c(B,t) are rational functions, then c(R,t) is also rational. If c(A,t) is rational and c(B,t) is algebraic, then c(R,t) is also algebraic. The proof is based on the fact that the product of two exponential generating functions behaves as the exponential generating function of the sequence of the degrees of the outer tensor products of two sequences of representations of symmetric groups.

Affiliated with

Also associated with

No associations

Rating

Algebraic Properties of Codimension Series of PI-Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algebraic Properties of Codimension Series of PI-Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic Properties of Codimension Series of PI-Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-327063