arithmetic in algebras, Adèle rings and groups, Infinite-dimensional simple rings (except as in 16Kxx), Quaternion and other division algebras: arithmetic, zeta functions, Finite rings and finite-dimensional associative algebras, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), decomposition of semisimple finite dimensional algebras, Linear algebraic groups over adèles and other rings and schemes, linear groups about adele groups