Abelian regular subgroups of the affine group and radical rings

By Andrea Caranti, F. Volta, M. Sala. Publicationes mathematicae (Debrecen), 2005

68 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/9010928588780fa32ab9fc8fbf0cfe20d3ecf88e

Citations in the corpus

• Bi-skew braces and Hopf Galois structures (2019, unknown): “This connection evolved from the discovery by [7] of the relationship between radical algebras and regular subgroups of the affine group, and its subsequent generalization and application to abelian Hopf Galois structures on elementary abelian Galois extensions of fields in [13].”