S2-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 said to be a S2-ring or to satisfy Serre's condition S2 if: Every associated prime of a [[[principal ideal]] generated by a non-zerodivisor in the ring is of codimension, and every associated prime of the zero ideal is of codimension 0.

Relation with other properties

Related properties

• R0-ring
• R1-ring
• S1-ring