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Proposition: Uniqueness of the Neutral Element
Let $(X,\ast)$ be an algebraic structure with at least one neutral element $e\in X.$ Then exactly one $e\in X$ is neutral.
- This proposition holds in all algebraic structures having a neutral element.
- Thus, the proof is the same for groups, unit rings, and fields.
Table of Contents
Definitions: 1 2 3 4 5
Proofs: 6 7 8 9
- Fischer, Gerd: "Lehrbuch der Algebra", Springer Spektrum, 2017, 4th Edition