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.

Caranti, A., DALLA VOLTA, F., Sala, M. (2006). Abelian regular subgroups of the affine group and radical rings. PUBLICATIONES MATHEMATICAE, 69(3), 297-308.

Abelian regular subgroups of the affine group and radical rings

DALLA VOLTA, FRANCESCA;
2006

Abstract

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.
Articolo in rivista - Articolo scientifico
affine group, abelian regular subgroups, (Jacobson) radical rings.
English
2006
69
3
297
308
none
Caranti, A., DALLA VOLTA, F., Sala, M. (2006). Abelian regular subgroups of the affine group and radical rings. PUBLICATIONES MATHEMATICAE, 69(3), 297-308.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/2478
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