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Proposition: Uniqueness of Inverse Elements

Let $(X,\ast)$ be an algebraic structure with an associative binary operation $[\ast".$ Let $x\in X$. If an inverse element of $x$ exists then it is unique.

Notes

• This proposition holds in all algebraic structures, in which the existence of inverse elements is postulated.
• Thus, the proof is the same for groups, unit rings, and fields.

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1 2 3
Proofs: 4 5 6

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