Torsion Free Modules in Which Every Proper Homorphism Image is Torsion
Received:November 30, 1987  
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Xin Lin 福建师范大学数学系 
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Abstract:
      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. NG= (0≠M∈F|M/L∈T for every nonzero submodu-le L?M} . then, M∈NG 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∈NG then M, MG∈NG.Fi-nally, we considered critically compressible modules, under the assumption that Gabriel topology G is perfect.
Citation:
DOI:10.3770/j.issn:1000-341X.1989.04.025
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