Proper ideal
From Commalg
This article is about a basic definition in commutative algebra. View a complete list of basic definitions in commutative algebra
This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings
Definition
Symbol-free definition
An ideal in a commutative unital ring is termed a proper ideal if it satisfies the following equivalent conditions:
- The element
of the ring, does not lie inside the ideal
- The ideal is not equal to the whole ring
Definition with symbols
An ideal in a commutative unital ring
is termed a proper ideal if it satisfies the following equivalent conditions: