First of all, we want to define formally, what exactly shall be understood under an algebraic structure. We start with the concept of a binary operation.

# Definition: Binary Operation

A binary operation $$\ast$$ on a set $$X$$ ist a total function $\ast :X\times X\to X$ mapping all pairs $x,y\in X\times X$ to a specific $z\in X,$ formally $$x\ast y:=\ast (x,y)=z.$$

Branches: 1
Chapters: 2 3
Corollaries: 4 5
Definitions: 6 7 8 9 10 11 12 13 14 15 16 17 18
Lemmas: 19
Motivations: 20
Problems: 21
Proofs: 22

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück