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We prove that every group ring of a non-abelian locally free group which isthe 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. Inaddition, by making use of the result, we give a necessary and sufficientcondition for group rings of ascending HNN extensions of free groups to beprimitive, which extends the known result for the countable case to the generalcardinality case. In order to prove the main theorem, we state somegraph-theoretic results and apply them to to Formanek's method.

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