Associative rings and algebras Radicals Concept
Prime radical
Summary
The prime radical of a ring is the intersection of all its prime ideals. It is also called the lower nilradical or the Baer radical. For a commutative ring it is the nilradical. It is the smallest of the classical radicals of a noncommutative ring, and it vanishes exactly for semiprime rings.
Further reading
About this page
| Tag | WF117EJ2HF |
|---|---|
| URI | m2://WF117EJ2HF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16N40, 16N60 |
| Changed | 2 November 2026 |
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