This article is about a basic definition in commutative algebra. View a complete list of basic definitions in commutative algebra
This article gives a property that can be evaluated for a subset of a ring
- It is a submodule of the ring viewed as a module over itself
- It is an Abelian group under addition and the product of any element in the ideal with any element in the ring lies in the ideal
- It occurs as the kernel of a ring homomorphism
Definition with symbols
An ideal in a commutative ring is a subset that satisfies the following equivalent conditions:
- an -submodule of .
- is an Abelian group under addition and further, is contained inside .