查看文章

Let M-R be a module with S = End(M-R). We call a submodule K of M-R annihilator-small if K + T = M, T a submodule of M-R, implies that l(S)(T) = 0, where l(S) indicates the left annihilator of T over S. The sum A(R)(M) of all such submodules of M-R contains the Jacobson radical Rad(M) and the left singular submodule Z(S)(M). If M-R is cyclic, then A(R)(M) is the unique largest annihilator-small submodule of M-R. We study A(R)(M) and K-S(M) in this paper. Conditions when A(R)(M) is annihilator-small and K-S(M) = J(S) = Tot(M, M) are given.