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.

  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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