摘要
R是一个环,C是包含内射左R-模的一个左R-模类,F是包含投射左R-模的一个左R-模类.本文给出若M的C-包络存在,则单态射i:M→C是M的C-包络当且仅当i是一个⊥C-本质扩张且C∈C.进一步我们讨论了在N≤_e M或者N≤M时,C(N)=C(M)的条件.最后,研究了C-包络的对偶的情形(F-覆盖).
Let R be a ring,C a class of left R-modules which contains all injective left R-modules and F a class of left R-modules which contains all projective left R-modules. It is proved that if the C-envelope of M exists,then a monomorphism i：M→C is a C-envelope of M if and only if i is a ~⊥C-essential extension of M and C∈C.Then we investigate when C（N） = C（M） under the condition N≤_e M or N≤M.Furthermore, the dual case,C-covers,is considered.
出处
《南京大学学报（数学半年刊）》
CAS
2010年第2期203-217,共15页
Journal of Nanjing University(Mathematical Biquarterly)
基金
supported by the National Natural Science Foundation of China(10871042,10971024)
the Specialized Research Fund for the Doctoral Program of Higher Education(200802860024)
