◀ ▲ ▶Branches / Algebra / Proposition: Uniqueness of Inverse Elements
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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