Topology & Geometric Group Theory Seminar

Spring 2010

1:30 – 2:30, Malott 203

Tuesday, February 16

Bogdan Petrenko, SUNY Brockport

On the smallest number of generators and the probability of generating an algebra

This talk is intended as an overview of my joint work with R. Kravchenko and M. Mazur (arXiv:1001.2873). That preprint addresses the following 2 related topics.

  1. Let R be an order in a number field. Let A be an R-algebra whose additive R-module is free of finite rank. What is the probability that k random elements of A generate it as an R-algebra? After making this question precise I will show that it has an interesting answer which can be interpreted as a local-global principle.
  2. We would like to calculate the smallest number of generators of such an algebra. We have complete answers for the R-algebras M2(R)k and M3(R)k, where R is the ring of integers in a number field and k is a positive integer.

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