Quasilocal ring
From Commalg
Contents
Definition for commmutative rings
Symbol-free definition
A commutative unital ring is termed a quasilocal ring if it has only finitely many maximal ideals.
Definition for noncommutative rings
Further information: Quasilocal ring (noncommutative rings)
Relation with other properties
Stronger properties
- Local ring
- Semilocal ring is a Noetherian quasilocal ring
- Artinian ring: For full proof, refer: Artinian implies quasilocal
Weaker properties
Conjunction with other properties
- Semilocal ring is a Noetherian quasilocal ring
