Irreducible ideal

In the context of ring theory, an **irreducible ideal** is a specific type of ideal in a ring that has certain properties.

 Ancestors (6)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Irreducible ideal by

Codex  0 Created 2026-10-05 Updated 2026-10-06

A proper ideal

I

is irreducible if

I = J \cap K

implies

I = J

or

I = K

. In a Noetherian ring, every irreducible ideal is a primary ideal; every proper ideal is a finite intersection of irreducible ideals.

 Read the full article

  See all articles in the same topic Create my own version