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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.

| | | | created: 2014-02-20 21:45:58 | modified: 2019-08-04 07:51:33 | by: bookofproofs

1.Definition: Binary Operation

2.Definition: Algebraic Structure (Algebra)

3.Important Properties of Binary Operations

4.Explanation: Operation Table

5.Magmas, Semigroups, Monoids (Overview)

6.Groups (Overview)

7.Rings (Overview)

8.Fields (Overview)

9.Vector Spaces (Overview)

10.Modules (Overview)

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)