Theorems in ring theory

Double centralizer theorem

In the branch of abstract algebra called ring theory, the double centralizer theorem can refer to any one of several similar results. These results concern the centralizer of a subring S of a ring R, denoted CR(S) in this article. It is always the case that CR(CR(S)) contains S, and a double centralizer theorem gives conditions on R and S that guarantee that CR(CR(S)) is equal to S. (Wikipedia).

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Simple ring | Division ring | Annihilator (ring theory) | Artinian ring | Polynomial identity ring | Primitive ring | Von Neumann bicommutant theorem | Schur's lemma | Simple module | Von Neumann algebra | Jacobson density theorem | Ring theory | Hilbert space | Abstract algebra | Balanced module | Kernel (algebra) | Weak operator topology | Centralizer and normalizer | Central simple algebra