拟对偶双边模和对偶双边模

摘要

A quasi-dual bimodule sMR can be characterized as every essential submodule K of MR and everyessential left ideal L of S which satisfy rMls (K)=K and lsrM(L) = L respectively. The relations are discussed between quasidual bimodules and dual-bimodules;a left quasi-dual bimodule is a left dual bimodule if it satisfies one of the following conditions:(i) sM is minimal injective and Ma is a M- minimal injective kasch- module; (ii) MR is a M-minimal injective kasch - module and rM ( L1∩L2 )= rM (L1)+rM (L2) for any two ideals L1 and L2 of sS;(iii) sM is minimal injective and for any two submodules A and B of Ma,Is(A∩B) =Is(A) +Is(B).%拟对偶双边模sMR可以被刻画成MR的每一个本质子模K和S的所有本质左理想L分别满足rMls(K)=K和lsrM(L)=L.拟对偶双边模和对偶双边模的关系表明:一个左拟对偶双边模sMR如果满足下列条件之一,则它成为坐对偶双边模:(1)sM是单内射的并且MR是一个M-单内射kasch-模;(2)MR是一个M-单内射kasch-模并且对sS的任意2个理想L1和L2有rM(L1∩L2)=rM(L1)+rM(L2);(3)SM是单内射的并且对MR的任意2个子模A和B,有ls(A∩B)=ls(A)+ls(B).