Associative rings and algebras Basic notions Concept
Center of a ring
Summary
The center of a ring is the set of elements that commute with every element of the ring. It is a commutative subring, and the ring is commutative exactly when its center is the whole ring. Every ring is an algebra over its center, which is why the center is the natural base ring in the study of noncommutative rings. It is the ring analogue of the centre of a group.
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| Tag | MVT64B3B6H |
|---|---|
| URI | m2://MVT64B3B6H |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16U70 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Central polynomial
- Kaplansky's theorem on PI rings
- Central simple algebra
- Posner's theorem
- Cartan–Brauer–Hua theorem