Free, projective, and flat modules and ideals in associative algebras, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), quasi-semiperfect modules, Noncommutative local and semilocal rings, perfect rings, semiperfect modules, lifting property of submodules, direct summands, generalized Krull-Remak-Schmidt-Azumaya theorem, quasi-projective modules, 16A50, lifting property of direct sums, 16A51, semiperfect rings, direct sums of hollow modules, direct decompositions