We classify semi-topological locally compact and semi-algebraic near-rings R where the set of non-invertible elements of R forms an ideal I of R such that the multiplicative group of R/I acts sharply transitively on I\{0}. To achieve our results we use as a main tool the classi cation of locally compact and algebraic (2; 2)-transformation groups given in two previuos papers.
Falcone, G., Di Bartolo, A., Strambach, K. (2013). NEAR-RINGS AND GROUPS OF AFFINE MAPPINGS. HOUSTON JOURNAL OF MATHEMATICS, 39(3), 753-780.
NEAR-RINGS AND GROUPS OF AFFINE MAPPINGS
FALCONE, Giovanni;DI BARTOLO, Alfonso;
2013-01-01
Abstract
We classify semi-topological locally compact and semi-algebraic near-rings R where the set of non-invertible elements of R forms an ideal I of R such that the multiplicative group of R/I acts sharply transitively on I\{0}. To achieve our results we use as a main tool the classi cation of locally compact and algebraic (2; 2)-transformation groups given in two previuos papers.
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