University of Guilan Journal of Algebra and Related Topics 2345-3931 12 1 2024 07 01 Modular representation of symmetric $2$-designs 79 87 7860 10.22124/jart.2024.22372.1407 EN O. Shimabukuro Department of Mathematics, Faculty of Education, Nagasaki University, Nagasaki, Japan Journal Article 2022 05 26 Complementary pairs of symmetric $2$-designs are equivalent to coherent configurations of type $(2, 2; 2)$.<br />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.<br />  coherent configuration symmetric design p-rank modular adjacency algebra modular standard module https://jart.guilan.ac.ir/article_7860_04560abcae377d10d87b831d87d4bba3.pdf