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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.

Notes

• 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

Proofs: 1

Mentioned in:

Definitions: 1 2 3 4 5
Proofs: 6 7 8 9

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References

Bibliography

1. Fischer, Gerd: "Lehrbuch der Algebra", Springer Spektrum, 2017, 4th Edition