We establish a link between regular subgroups of the affine group and radical circle algebras on the underlying vector space.2000 Mathematics subject classification: 20B10, 16N20.
Let A be a non-trivial semiprime associative superalgebra with superinvolution. In the present note we investigate when the subspaces of symmetric elements or skew elements of A are Lie nilpotent or Lie solvable. We show that these conditions determine the algebraic structure of A
We study semiprime superalgebras with superinvolution whose symmetric or skewsymmetric elements are assumed to be regular or nilpotent, and superalgebras in which xx* = 0 implies x*x = 0.
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