O. Shimabukuro - Department of Mathematics, Faculty of Education, Nagasaki University, Nagasaki, Japan

Complementary pairs of symmetric ۲-designs are equivalent to coherent configurations of type (۲, ۲; ۲).D. G. Higman studied these coherent configurations and adjacency algebras of coherent configurations over a field of characteristic zero. These are always semisimple.  We investigate these algebras over fields of any characteristic prime and the structures.

coherent configuration, symmetric design, p-rank, modular adjacency algebra, modular standard module