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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).

Table of Contents

Proofs: 1

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References

Bibliography

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