Group rings of countable non-abelian locally free groups are primitive

Details Group rings of countable non-abelian locally free groups are primitive Group rings of countable non-abelian locally free groups are primitive

2010-10-23

arxiv.org/abs/1010.4898v1

Mathematics

Rings and Algebras

27 pages, to appear in International Journal of Algebra and Computation

Scientific paper

We prove that every group ring of a non-abelian locally free group which is the union of an ascending sequence of free groups is primitive. In particular, every group ring of a countable non-abelian locally free group is primitive. In addition, by making use of the result, we give a necessary and sufficient condition for group rings of ascending HNN extensions of free groups to be primitive, which extends the known result for the countable case to the general cardinality case. In order to prove the main theorem, we state some graph-theoretic results and apply them to to Formanek's method.

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