Nil element

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


An element n in a magma (S,*) is termed a:

  • left nil element if n * a = n for all a \in S.
  • right nil element if a * n = n for all a \in S.
  • nil element if it is both a left nil element and a right nil element.

If both a left nil and a right nil exist, they are equal. For full proof, refer: Equality of left and right nil element