Jacobson density theorem

Let $U$ be a simple right $R$ module, and $D$ be the ring of endomorphisms of $U$. If $A$ is any $D$ linear operator and $X$ is any finite subset of $R$, there exists $r\in R$ such that $xr=xA$ for all $x\in X$. As a corollary every right (left) primitive ring is a dense subring of a ring of linear transformations.



  • F. W. Anderson and K. R. Fuller. Rings and categories of modules. (2012) @ Chapter 4
  • N. Jacobson. Basic algebra II. (2012) @ Section 4.3