Group rings of countable non-abelian locally free groups are primitive
Group rings of countable non-abelian locally free groups are primitive
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可数非阿贝尔局部自由群的群环是原始群
DOI：
10.1142/s0218196711006273
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Tsunekazu Nishinaka
中科院分区：
文献类型：
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作者：
小池寿俊;(書評) Y. Baba and K. Oshiro;K. Oshiro;小池寿俊;Tsunekazu Nishinaka;Tsunekazu Nishinaka;Tsunekazu Nishinaka
本文证明了非交换局部自由群的每一个群环都是本原的，它是自由群的升序列的并。特别地，可数非交换局部自由群的每个群环都是本原的。另外，利用这个结果，我们给出了自由群的升HNN扩张的群环是本原的一个充要条件，将[Group rings of proper ascending HNN extensions of countably infinite free groups are primitive，J. Algebra 317（2007）581-592]中的主要结果推广到了一般基数情形.
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. Algebra317(2007) 581–592] to the general cardinality case.