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Difference between revisions of "Identity element"

From Encyclopedia of Mathematics
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(Start article: Identity element)
 
(also called unit element)
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''neutral element''
+
''neutral element'', ''zero element''
  
 
An element of an algebraic structure $S$, often denoted $1$, $I$ or $e$, with a specific property with respect to a [[binary operation]] $*$:
 
An element of an algebraic structure $S$, often denoted $1$, $I$ or $e$, with a specific property with respect to a [[binary operation]] $*$:

Revision as of 18:27, 13 December 2014

neutral element, zero element

An element of an algebraic structure $S$, often denoted $1$, $I$ or $e$, with a specific property with respect to a binary operation $*$: $$ \forall x \in S \ \ 1 * x = x * 1 = x\ . $$

Where the binary operation is written additively, the identity element may be denoted $0$ or $O$, and termed a zero element.

How to Cite This Entry:
Identity element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Identity_element&oldid=35629