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Definition: Cancellation Property

An algebraic structure $(X,\ast)$ is said to have

• the left cancellation property, if for all elements $x,y,a\in G$ the equation $a\ast x=a\ast y$ always implies $x=y$ and
• the right cancellation property, if for all elements $x,y,a\in G$ the equation $x\ast a=y\ast a$ always implies $x=y$.

If $(X,\ast)$ has both, the left and the right cancellation property, then it is called cancellative.

Mentioned in:

Chapters: 1 2 3 4
Parts: 5
Proofs: 6 7 8 9 10 11 12 13 14 15 16 17
Propositions: 18 19 20 21 22 23 24 25 26 27 28 29 30
Theorems: 31

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References

Bibliography

1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013