Injective Hull - Examples

Examples

  • The injective hull of an injective module is itself.
  • The injective hull of an integral domain is its field of fractions, (Lam 1999, Example 3.35)
  • The injective hull of a cyclic p-group (as Z-module) is a Prüfer group, (Lam 1999, Example 3.36)
  • The injective hull of R/rad(R) is Homk(R,k), where R is a finite dimensional k-algebra with Jacobson radical rad(R), (Lam 1999, Example 3.41).
  • A simple module is necessarily the socle of its injective hull.

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