摘要
设R是有单位的结合环,在不特别指明时,R-模均指右模。R上的右理想集合G称为Gabriel拓扑,如果非空集G满足条件: ⅰ) A∈G,b∈R,则(A:b)∈G,这里(A:b)={r∈R|br∈A}。 ⅱ) 如果B是R的右理想并且有A∈G使得(B:a)∈G,a∈A,则B∈G。 设(T,F)是相应于G的torsion theory。我们知道:T中模称为挠模。
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 .
