Difference between revisions of "Identity element"
From Encyclopedia of Mathematics
(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
Identity element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Identity_element&oldid=35629