Аннотация:
The Kaplansky conjectures are three long-standing open problems on the group rings of torsion-free groups. In this talk we consider the zero divisor conjecture: Let G be a torsion-free group then the group ring Z[G] has no non-trivial zero divisors, i.e., it is a domain. This problem is an old one, and there are several results that confirm it, for some classes of groups. However, there is no unique method or way to attack it. In this talk, we discuss a way suggested by Roman Mikhailov. This way is based on an exact sequence arising in homological group theory. This way is still complicated but seems hopeful.
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