关于 ann-内射模和ann-平坦模

摘要

A left R-module E is ann-injective provided that every R-homomorphism from an finitelygenerated right annihilator ideal r(L) of R to E can be extended to R. We say that a left R-module M is ann-flat in case for every finitely generated right annihilator ideal r(L) of R,we have the exact sequence 0→r(L) (×)RM→RR(×)M. In this articfle, we prove that a left R--module B is ann--flat if and only if itscharacteristic module B* =HmomR(B,Q/Z) is ann--injective.%左 R-模 E 是 ann-内射的,如果对于R的每个有限生成右零化子理想r(L)到R的R-模同态都能延拓为到E的 R-模同态.同样.我们称左R-模M是ann-平坦的如果对于R的每个有限生成右零化子理想r(L),都可以得到正合列O→r(L) (×)RM→RR(×)M.在本文中,我们证明了R-模B是ann-平坦的当且仅当它的示性模B*=HomR(B,Q/Z)是ann-内射的.