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Chapter: Divisibility in General Rings

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.

Table of Contents

1. Definition: Zero Divisor and Integral Domain
2. Proposition: Generalization of Cancellative Multiplication of Integers
3. Definition: Generalization of Divisor and Multiple
4. Definition: Generalization of the Greatest Common Divisor
5. Definition: Generalization of the Least Common Multiple
6. Definition: Unit
7. Definition: Associate
8. Definition: Irreducible, Prime
9. Definition: Factorial Ring, Generalization of Factorization
10. Definition: Euclidean Ring, Generalization of Division With Quotient and Remainder
11. Section: Ideals
12. Lemma: Factor Rings, Generalization of Congruence Classes

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