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Definition: Monoid

A monoid is a semigroup \((X,\ast)\) with an identity, i.e. an element $e\in X$ with $x=e\ast x=x\ast e$ for all $x\in X.$

Please note the uniqueness of the neutral element $e\in X$.

Mentioned in:

Axioms: 1
Chapters: 2 3 4 5
Corollaries: 6
Definitions: 7 8 9 10
Examples: 11
Parts: 12
Proofs: 13 14 15 16
Propositions: 17

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References

Bibliography

1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001

Adapted from CC BY-SA 3.0 Sources:

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