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Theorem: Connection between Rings, Ideals, and Fields
 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).
 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
 Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013