Integral Domain

Dependencies:

  1. Ring

$R$ is an integral domain iff it is a commutative ring with no zero-divisors.

$a, b \in R-\{0\}$ are zero-divisors iff $ab = 0$.

Consequently, an integral domain has at least 2 elements, 0 and 1.

Dependency for:

  1. I is a prime ideal iff R/I is an integral domain
  2. Zp is an integral domain
  3. A field is an integral domain
  4. A finite integral domain is a field
  5. Comparing coefficients of a polynomial with disjoint variables

Info:

Transitive dependencies:

  1. Group
  2. Ring