Binary operation on magma determines neutral element

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Revision as of 21:46, 31 July 2008 by Vipul (talk | contribs) (New page: ==Statement== Suppose <math>(S,*)</math> is a magma (set <math>S</math> with associative binary operation <math>*</math>). Then, if there exists a neutral element for <math>*</mat...)
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Statement

Suppose (S,*) is a magma (set S with associative binary operation *). Then, if there exists a neutral element for * (i.e., an element e such that e * a = a * e = a for all a \in S), the element e is uniquely determined by *.

In other words, a magma can have at most one two-sided neutral element.

Facts used

Equality of left and right neutral element