GROUP RINGS OF COUNTABLE NON-ABELIAN LOCALLY FREE GROUPS ARE PRIMITIVE

作者：Nishinaka Tsunekazu^*

来源：International Journal of Algebra and Computation, 2011, 21(3): 409-431.

DOI：10.1142/S0218196711006273

• Group ring
• primitive
• locally free group
• ascending HNN-extension

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 main result in [Group rings of proper ascending HNN extensions of countably infinite free groups are primitive, J. Algebra 317 (2007) 581-592] to the general cardinality case.

• 出版日期2011-5