Regular direct products of affine partial linear spaces (Q2474150)

Continuing their investigations begun in [J. Geom. 83, 175--195 (2005; Zbl 1093.51004)], the authors determine the class of all maximal affine Baer substructures of a regular direct product \(\mathfrak{E}^I\) (a notion introduced by \textit{N. L. Johnson} and \textit{T. G. Ostrom} [J. Comb. Theory, Ser. A 75, No. 1, 99--140 (1996; Zbl 0873.51001)]) of a Desarguesian affine space \(\mathfrak{E}\) (and show both that \(\mathfrak{E}^I\) needs to be Desarguesian in this case, and that this fact need not hold if \(\mathfrak{E}\) were only a Desarguesian partial linear space with parallelism).