A Note on Group Rings of Certain Torsion-Free Groups
A Note on Group Rings of Certain Torsion-Free Groups
复制标题
关于某些无扭组的组圈的注解
DOI：
--
复制
发表时间：
1972
期刊：
影响因子：
--
通讯作者：
V. W. Hale
中科院分区：
文献类型：
--
作者：
Robert G. Burns;V. W. Hale
摘要作为表征ID组的一步（即，群G使得对于每个不含零因子的环R，群环RG不含零因子），Rudin和Schneider定义了Ω-群，这是一个可能比右可序群更广的类，并证明了如果群G的每个非平凡生成子群都有一个非平凡H-群作为满射像，则G是ID-群。证明了这类群是偶Ω-群，并得到了右可序群的类似结果。
Abstract As a step towards characterizing ID-groups (i.e., groups G such that, for every ring R without zero-divisors, the group ring RG has no zero-divisors), Rudin and Schneider defined Ω-groups, a possibly wider class than that of right-orderable groups, and proved that if every non-trivial finitely generated subgroup of a group G has a non-trivial H-group as an epimorphic image, then G is an ID-group. We prove that such groups are even Ω-groups and obtain the analogous result for right-orderable groups.