Theorem B (modules) Let M be a module, and let S and T be submodules of M. Then: The sum S + T = {s + t | s ∈ S, t ∈ T} is a submodule of M, The intersection S ∩ T is a submodule of M, and The quotient modules (S + T) / T and S / (S ∩ T) are isomorphic.
THeOrem b (modules) let m be a mOdulE, aNd LEt s ANd T bE SuBMOdules oF M. then: tHe SUM S + t = {S + t | S ∈ S, t ∈ t} is a subModUle oF m, the inteRsEcTIon s ∩ t iS A SUbmodule Of m, anD ThE QuotiEnt moDules (s + T) / T anD s / (s ∩ t) are ISoMoRPHic.