◀ ▲ ▶Branches / Algebra / Definition: Cancellation Property
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
- Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013
