In the following chapter, we will generalize the results we achieved in the elementary number theory about divisibility for the set $\mathbb Z$ of integers to generalize integral domain.

- Definition: Zero Divisor and Integral Domain
- Proposition: Generalization of Cancellative Multiplication of Integers
- Definition: Generalization of Divisor and Multiple
- Definition: Generalization of the Greatest Common Divisor
- Definition: Generalization of the Least Common Multiple
- Definition: Unit
- Definition: Associate
- Definition: Irreducible, Prime
- Definition: Factorial Ring, Generalization of Factorization
- Definition: Euclidean Ring, Generalization of Division With Quotient and Remainder
- Section: Ideals
- Lemma: Factor Rings, Generalization of Congruence Classes