Integral Domain - Properties

Properties

  • Let R be an integral domain. Then there is an integral domain S such that R ⊂ S and S has an element which is transcendental over R.
  • The cancellation property holds in integral domains. That is, let a, b, and c belong to an integral domain. If a ≠ 0 and ab = ac then b = c. Another way to state this is that the function x ↦ ax is injective for any non-zero a in the domain.
  • An integral domain is equal to the intersection of its localizations at maximal ideals.
  • An inductive limit of integral domains is an integral domain.

Read more about this topic:  Integral Domain

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