Articles containing proofs | Theorems in ring theory | Module theory

Jacobson density theorem

In mathematics, more specifically non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem can be applied to show that any primitive ring can be viewed as a "dense" subring of the ring of linear transformations of a vector space. This theorem first appeared in the literature in 1945, in the famous paper "Structure Theory of Simple Rings Without Finiteness Assumptions" by Nathan Jacobson. This can be viewed as a kind of generalization of the Artin-Wedderburn theorem's conclusion about the structure of simple Artinian rings. (Wikipedia).

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Related pages

Simple ring | Linear span | Annihilator (ring theory) | Artinian ring | Primitive ring | Dense set | Von Neumann bicommutant theorem | Schur's lemma | Mathematics | Simple module | Kaplansky density theorem | Mathematical induction | Ring theory | Hilbert space | Abstract algebra | Subspace topology | Weak operator topology | Endomorphism | Product topology