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{{main|Jacobson density theorem}}
An important advance in the theory of simple modules was the [[Jacobson density theorem]]. The Jacobson density theorem states:
:Let ''U'' be a simple right ''R''-module and let ''D'' = End<sub>''R''</sub>(''U''). Let ''A'' be any ''D''-linear operator on ''U'' and let ''X'' be a finite ''D''-linearly independent subset of ''U''. Then there exists an element ''r'' of ''R'' such that ''x''&
In particular, any [[primitive ring]] may be viewed as (that is, isomorphic to) a ring of ''D''-linear operators on some ''D''-space.
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