真同态像都是挠模的挠自由模

Torsion Free Modules in Which Every Proper Homorphism Image is Torsion

中文摘要:

      

英文摘要:

      This paper is devoted to proving the following fact :Let G be a Gabriel topology, E an injective module cogenerating torsion theory (T, F) associated to G. N_G= (0≠M∈F|M/L∈T for every nonzero submodu-le L?M} . then, M∈N_G if and only if1) M is uniform,2) every nonzero homomorphism form M into M is injective,3) M is a quasi-essential submodule of E.At the same time, we proved that if a module M∈N_G then M, M_G∈N_G.Fi-nally, we considered critically compressible modules, under the assumption that Gabriel topology G is perfect.