Non-associative algebra | Algebraic properties of elements | Properties of binary operations

Cancellation property

In mathematics, the notion of cancellative is a generalization of the notion of invertible. An element a in a magma (M, ∗) has the left cancellation property (or is left-cancellative) if for all b and c in M, a ∗ b = a ∗ c always implies that b = c. An element a in a magma (M, ∗) has the right cancellation property (or is right-cancellative) if for all b and c in M, b ∗ a = c ∗ a always implies that b = c. An element a in a magma (M, ∗) has the two-sided cancellation property (or is cancellative) if it is both left- and right-cancellative. A magma (M, ∗) has the left cancellation property (or is left-cancellative) if all a in the magma are left cancellative, and similar definitions apply for the right cancellative or two-sided cancellative properties. A left-invertible element is left-cancellative, and analogously for right and two-sided. For example, every quasigroup, and thus every group, is cancellative. (Wikipedia).

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Related pages

Integral domain | Cancellative semigroup | Quasigroup | Group (mathematics) | Determinant | Semigroup | Equation | Mathematics | Real number | Ring (mathematics) | Cross product | Abstract algebra | Complex number | Matrix multiplication | Magma (algebra) | Domain (ring theory) | Matrix (mathematics) | Elementary algebra | Grothendieck group | Monoid