Re: is every ideal of a ring an annihilator of an element of some module?
Originally Posted by ymar
Let be a right ideal of a ring Is there always a right module and such that
I assume that our rings are unital, no? Note then that has a natural -module structure. If then we see that since for all and so . Conversely, if then , so that , etc.
EDIT: Misread to try and prove that , but NonCommAlg read it correctly. Same idea though.