Associative rings and algebras Basic notions Concept
Nil ideal
Summary
A nil ideal of a ring is a one-sided or two-sided ideal all of whose elements are nilpotent. Nil ideals are a main object of radical theory, the study of the parts of a ring that are discarded to reach simpler rings. In a commutative ring the largest nil ideal is the nilradical. Whether every nil one-sided ideal lies in a nil two-sided ideal is the open Köthe conjecture.
Where this leads
6 pages build on this one.
Further reading
About this page
| Tag | NZ1G9WRWFB |
|---|---|
| URI | m2://NZ1G9WRWFB |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16N40 |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Kurosh problem
- Nilpotent ideal
- Levitzki's theorem
- Köthe conjecture
- Upper nilradical
- Amitsur's theorem on the radical of polynomial rings