【摘要】 对全不变子模的两个定理:1.设M是右R-模,M=M1 M2,若N≤SMR,那么N=N1 N2,其中Ni=N∩Mi≤S(Mi)R,i=1,2;2.设M是右R-模,M=M1 M2,若F1≤S(M1)R,那么存在F2≤S(M2)R,使得F1 F2≤SMR.进行推广,则为:1’.设M是右R-模,M= i∈ΛMi,若N≤SMR,那么N= i∈ΛNi,其中Ni=N∩Mi≤S(Mi)R,i∈Λ;2’.设M是右R-模,M= i∈ΛMi,若F1≤S(M1)R,那么存在Fi≤S(Mi)R,i∈Λ-{1},使得 i∈ΛFi≤SMR.更多还原

【Abstract】 Two theorems concerning fully invariant submodules: 1, Let M be a right R-module, and let M=M₁M₂, be a direct sum decomposition. If N≤_SM_R, then N=N₁N₂, where N_i=N∩M_i≤_S（M_i）_R, i=1, 2; and 2, Let M be a right R-module, with M=M₁M₂, and let F₁≤_S（M₁）_R. Then there exists F₂≤_S（M₂）_R, so that F₁F₂≤_SM_R are generalized as:1’,Let M be a right R-module and let M=_i∈ΛM_i bea direct sum decomposition, for an index i∈Λ. If N≤_SM_R, then N=_i∈ΛN_i, where N_i=N∩M_i≤_S（M_i）_R, i∈Λ; and 2’, Let M be a right R-module , with M=_i∈ΛM_i ,for an index set Λ, and let F₁≤_S（M₁）_R, Then there exists F_i≤_S（M_i）_R,i∈Λ-{1}, so that (i∈ΛFi≤_SM_R.更多还原