FA-presentable groups and rings
FA-presentable groups and rings
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FA-可表示的群和环
DOI：
10.1016/j.jalgebra.2007.04.015
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发表时间：
2008
影响因子：
0.9
通讯作者：
R. Thomas
中科院分区：
文献类型：
--
作者：
A. Nies;R. Thomas
我们考虑FA可表示的结构。众所周知，一个FA-presentable生成群几乎是阿贝尔的，我们加强这一结果表明，一个任意的FA-presentable组是本地几乎阿贝尔。因此，我们证明了任何FA-可表示环都是局部有限的;这是一个重要的限制，并允许我们对FA-可表示环的结构进行大量的讨论。特别地，我们证明了任何具有单位元且没有零因子的FA-可表示环都是有限的。
We consider structures which are FA-presentable. It is known that an FA-presentable finitely generated group is virtually abelian; we strengthen this result by showing that an arbitrary FA-presentable group is locally virtually abelian. As a consequence, we prove that any FA-presentable ring is locally finite; this is a significant restriction and allows us to say a great deal about the structure of FA-presentable rings. In particular, we show that any FA-presentable ring with identity and no zero divisors is finite.