Cancellative semigroup

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This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup
View a complete list of semigroup properties

Definition

Symbol-free definition

A cancellative semigroup (also called cancellation semigroup) is a semigroup where every element is cancellative.

Definition with symbols

A semigroup (S,*) (a set S with associative binary operation *) if the following hold for all a,b,c \in S:

  • a * b = a * c \implies b = c
  • b * a = c * a \implies b = c