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Thursday, March 13, 2014

**Abstract:** Let A be a ring whose additive group is free abelian of finite rank. The topic of this talk is the following question: what is the probability that several random elements of A generate it as a ring? After making this question precise I will show that it has an interesting answer which can be interpreted as a local-global principle. Some applications will be discussed. This talk will be based on my joint work with with Rostyslav Kravchenko (University of Chicago) and Marcin Mazur (Binghamton University).