Cancellative element

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This article defines a property of elements or tuples of elements with respect to a binary operation


An element a in a magma (S,*) (a set S with binary operation *) is termed:

  • left-cancellative if whenever a * b = a * c, b = c
  • right-cancellative if whenever b * a = c * a, b = c
  • cancellative if it is both left and right cancellative

A magma where every element is left-cancellative (resp. right-cancellative, cancellative) is termed a left-cancellative magma (resp., right-cancellative magma, cancellative magma).

Relation with other properties

Stronger properties