Blocking sets of Rédei type in projective Hjelmslev planes (Q982611)

In a projective plane PG\((2,q)\), a \textit{Rédei type} blocking set is a set of points of size \(q+k\) intersecting every line in at least one point and having at least one \(k\)-secant to it. These Rédei type blocking sets in PG\((2,q)\) have been investigated in great detail. In particular, there are the two results of \textit{A. Blokhuis, S. Ball, A. E. Brouwer} and \textit{T. Szőnyi} [J. Comb. Theory, Ser. A 86, No. 1, 187--196 (1999; Zbl 0945.51002)] and \textit{S. Ball} [J. Comb. Theory, Ser. A 104, No. 2, 341--350 (2003; Zbl 1045.51004)]. This paper generalizes the notion of Rédei type blocking sets in a projective plane PG\((2,q)\) to coordinate projective Hjelmslev planes over finite chain rings. A classical example of a Rédei type blocking set is the Baer subplane in a projective plane PG\((2,q)\) of square order \(q\). The authors construct in this article in Hjelmslev planes over chain rings of nilpotency index 2 that contain the residue field as a proper subring, Rédei type blocking sets by taking the Baer subplanes associated with this subring and using them to construct Rédei type blocking sets in the original Hjelmslev planes. Furthermore, two extra examples of Rédei type blocking sets are given for projective Hjelmslev planes over Galois rings that generalize known constructions of Rédei type blocking sets in projective planes PG\((2,q)\).