Nil element

From Groupprops
Revision as of 20:59, 31 July 2008 by Vipul (talk | contribs) (New page: {{magma-element property}} ==Definition== An element <math>n</math> in a magma <math>(S,*)</math> is termed a: * '''left nil element''' if <math>n * a = n</math> for all <math>a \in...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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

Definition

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