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Search: MSC category 16Y30 ( Near-rings [See also 12K05] )

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1. CMB 2006 (vol 49 pp. 347)

Ecker, J├╝rgen
Affine Completeness of Generalised Dihedral Groups
In this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for every $k \in~\N$ the $k$-affine complete generalised dihedral groups. We find that the direct product of a $1$-affine complete group with itself need not be $1$-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for $2$-affine completeness.

Categories:08A40, 16Y30, 20F05

2. CMB 1997 (vol 40 pp. 198)

Meldrum, J. D. P.; Meyer, J. H.
The ${\cal J}_0$-radical of a matrix nearring can be intermediate
An example is constructed to show that the ${\cal J}_0$-radical of a matrix nearring can be an intermediate ideal. This solves a conjecture put forward in [1].

Categories:16Y30, 16S50, 16D25

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