Thread: is every ideal of a ring an annihilator of an element of some module?

Let be a right ideal of a ring Is there always a right module and such that

Originally Posted by ymar

Let be a right ideal of a ring Is there always a right module and such that

yes, and

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.