Ideal

Dependencies:

1. Ring

Let $I$ be a subring of $R$.

• $I$ is a left ideal iff it follows left-absorption, i.e. $\forall a \in R, aI \subseteq I$.
• $I$ is a right ideal iff it follows right-absorption, i.e. $\forall a \in R, Ia \subseteq I$.
• $I$ is a two-sided ideal iff it is both a left ideal and a right ideal.

Dependency for:

1. I is a prime ideal iff R/I is an integral domain
2. I is a maximal ideal iff R/I is a field
3. Principal ideal
4. Product of ideal cosets is well-defined
5. p(x)F[x] = F[x] iff p is a non-zero constant

Info:

• Depth: 2
• Number of transitive dependencies: 2

Transitive dependencies:

1. Group
2. Ring