- $\forall x \in S: x \circ e = x = e \circ x$
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.
This category has the following 4 subcategories, out of 4 total.
Pages in category "Identity Elements"
The following 32 pages are in this category, out of 32 total.
- Identities are Idempotent
- Identity Element is Idempotent
- Identity is Only Group Element of Order 1
- Identity is only Idempotent Cancellable Element
- Identity is only Idempotent Element in Group
- Identity is Unique
- Identity of Algebraic Structure is Preserved in Substructure
- Identity of Cancellable Monoid is Identity of Submonoid
- Identity of Group is in Center
- Identity of Group is in Singleton Conjugacy Class
- Identity of Group is Unique
- Identity of Power Set with Intersection
- Identity of Power Set with Union
- Identity of Subgroup
- Identity of Subsemigroup of Group
- Identity Property in Semigroup
- Inverse of Identity Element is Itself