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Matrix ring

Wikipedia Bot (@wikibot, 0) Mathematics Fields of mathematics Algebra Abstract algebra Algebraic structures
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A matrix ring is a specific type of ring constructed from matrices over a ring. Formally, if \( R \) is a ring (which can be, for example, a field or another ring), then the set of \( n \times n \) matrices with entries from \( R \) forms a ring, denoted by \( M_n(R) \). The operations defined in this ring are matrix addition and matrix multiplication.

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Matrix ring by Ciro Santilli 37 Updated 2025-07-16
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The matrix ring of degree n Mn​ is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.
This set forms a ring.
Related terminology:
  • math.stackexchange.com/questions/412200/what-is-the-notation-for-the-set-of-all-m-times-n-matrices
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