Gabor Braun, Sebastian Pokutta. Rigid abelian groups and the probabilistic method
Natural Sciences / Mathematics / Algebra
Submitted on: Sep 13, 2012, 17:36:37
Description: The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups. Usually these construction work by adding elements from a (topological) completion in order to get rid of (kill) unwanted homomorphisms. The critical part is to actually prove that every unwanted homomorphism can be killed by adding a suitable element. We will demonstrate that some of those constructions can be significantly simplified by choosing the elements at random. As a result, the endomorphism ring will be almost surely prescribed, i.e., with probability one. ***Article was originally published in Contemporary Mathematcs 576 (2012), 17-30***