Category:Identity Elements

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This category contains results about Identity Elements in the context of Abstract Algebra.
Definitions specific to this category can be found in Definitions/Identity Elements.


An element $e \in S$ is called an identity (element) if and only if it is both a left identity and a right identity:

$\forall x \in S: x \circ e = x = e \circ x$


In Identity is Unique it is established that an identity element, if it exists, is unique within $\struct {S, \circ}$.

Thus it is justified to refer to it as the identity (of a given algebraic structure).


This identity is often denoted $e_S$, or $e$ if it is clearly understood what structure is being discussed.

Subcategories

This category has the following 3 subcategories, out of 3 total.