Identity element: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Richard Pinch
(→‎Examples: zero matrix)
imported>Richard Pinch
(subpages)
Line 1: Line 1:
{{subpages}}
In [[algebra]], an '''identity element''' or '''neutral element''' with respect to a [[binary operation]] is an element which leaves the other operand unchanged, generalising the concept of [[zero]] with respect to [[addition]] or [[one]] with respect to [[multiplication]].
In [[algebra]], an '''identity element''' or '''neutral element''' with respect to a [[binary operation]] is an element which leaves the other operand unchanged, generalising the concept of [[zero]] with respect to [[addition]] or [[one]] with respect to [[multiplication]].



Revision as of 15:33, 8 December 2008

This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In algebra, an identity element or neutral element with respect to a binary operation is an element which leaves the other operand unchanged, generalising the concept of zero with respect to addition or one with respect to multiplication.

Formally, let be a binary operation on a set X. An element I of X is an identity for if

holds for all x in X. An identity element, if it exists, is unique.

Examples

See also