Page "Primitive ring" Paragraph 9

Every simple ring R with unity is both left and right primitive.

( However, a simple non-unital ring may not be primitive.

) This follows from the fact that R has a maximal left ideal M, and the fact that the quotient module R / M is a simple left R-module, and that its annihilator is a proper two-sided ideal in R. Since R is a simple ring, this annihilator is