Semihereditary ring

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

Definition

Symbol-free definition

A commutative unital ring is termed semihereditary if every finitely generated ideal in it is projective as a module.

Relation with other properties

Stronger properties

• Field
• Semisimple Artinian ring
• Hereditary ring
• Dedekind domain
• Prufer domain