Part: Algebraic Structures - Overview

When we dealt with number systems, we became familiar for instance with the natural numbers together with addition $(\mathbb N, + )$, the integers together with addition and multiplication $(\mathbb Z, +, \cdot),$ or the real numbers together with addition and multiplication $(\mathbb R , + ,\cdot).$

In general, if on a set one or more operation, like addition or multiplication, is defined, usually these operations "shape" a structure inside the set, called an algebraic structure.

In this part, we start our treatise of algebra with a quick overview of the different algebraic structures. In later parts, we will dive deeper into the theory of the separate algebraic structures.

Motivations: 1 Explanations: 1

  1. Definition: Algebraic Structure (Algebra)
  2. Definition: Binary Operation
  3. Chapter: Important Properties of Binary Operations
  4. Chapter: Magmas, Semigroups, Monoids (Overview)
  5. Chapter: Groups (Overview)
  6. Chapter: Rings (Overview)
  7. Chapter: Fields (Overview)
  8. Chapter: Vector Spaces (Overview)
  9. Chapter: Modules (Overview)

Branches: 1
Chapters: 2
Definitions: 3 4
Motivations: 5 6

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