Theorem: Connection between Rings, Ideals, and Fields

  1. Every field $(F, + ,\cdot)$ has only the two ideals: $\{0\}\lhd F$ and $F\lhd F$ (i.e. the ideal $\{0\}$ consisting of only the zero element $0\in F$) and the field $F$ itself).
  2. Every field $(F, + ,\cdot)$ has only the two ideals: $\{0\}\lhd F$ and $F\lhd F$ (i.e. the ideal $\{0\}$ consisting of only the zero element $0\in F$) and the field $F$ itself).

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

  1. Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013