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Chapter: Important Properties of Binary Operations

Binary operations can have different properties and some of them are particularly important for algebraic structures. In fact, the kind of the resulting algebraic structure depends on the properties of the binary operations involved.

Table of Contents

  1. Definition: Closure
  2. Definition: Associativity
  3. Definition: Commutativity
  4. Definition: Existence of a Neutral Element
  5. Proposition: Uniqueness of the Neutral Element
  6. Definition: Inverse Element
  7. Proposition: Uniqueness of Inverse Elements
  8. Definition: Cancellation Property

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