Matrix ring Guide, Meaning , Facts, Information and Description

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

Properties

• 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.

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