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.

Let R be an order in a number field. Let A be an Ralgebra
whose additive Rmodule is free of finite rank. What is the
probability that k random elements of A generate it as an
Ralgebra? After making this question precise I will show that it
has an interesting answer which can be interpreted as a localglobal
principle.

We would like to calculate the smallest number of generators of
such an algebra. We have complete answers for the Ralgebras
M_{2}(R)^{k} and M_{3}(R)^{k},
where R is the ring of integers in a number field and k is a
positive integer.
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