Matrix ring

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In abstract algebra the matrix ring M(n,R) is set of all n×n matrices over an arbitrary ring R. This set is itself a ring under matrix addition and multiplication.

[edit] Properties

• A matrix ring over R is commutative if and only if n ≤ 1 or |R| = 1.
• A matrix ring over a division ring is a simple ring. There is a partial converse in the form of the Artin-Wedderburn theorem.
• A matrix ring over a prime ring is a prime ring.
• The matrix ring M(n,R) can be identified with the ring End(Z^n).