Associative rings and algebras Semisimple rings and Wedderburn theory Concept
Simple ring
Summary
A simple ring is a nonzero ring whose only two-sided ideals are and the whole ring. It cannot be broken into smaller rings by passing to quotients. Fields, division rings and full matrix rings over them are simple. By Wedderburn's theorem, the simple Artinian rings are exactly the matrix rings over division rings.
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About this page
| Tag | 62M0NC3E2T |
|---|---|
| URI | m2://62M0NC3E2T |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16D60, 16D25 |
| Specializes | Ring |
| Same as | |
| Changed | 2 November 2026 |
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Definitions
Used by
- Central simple algebra
- Double centralizer theorem
- Matrix rings over simple rings are simple
- Goldie's theorem
- Skolem–Noether theorem
- Wedderburn's theorem on simple Artinian rings