Abelian regular subgroups of the affine group and radical rings
Abelian regular subgroups of the affine group and radical rings
复制标题
仿射群和根环的阿贝尔正则子群
DOI：
10.5486/pmd.2006.3594
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发表时间：
2005
影响因子：
0.6
通讯作者：
M. Sala
中科院分区：
文献类型：
--
作者：
A. Caranti;F. Volta;M. Sala
We establish a link between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings.
As an application, we show that if the underlying field has positive characteristic, then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be torsion free if the dimension is infinite.
We also give an example of an abelian, regular subgroup of the affine group over an infinite vector space, which intersects trivially the group of translations.
