- $\forall x \in S: x \circ e = x = e \circ x$
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 8 subcategories, out of 8 total.
- Unity (empty)
Pages in category "Identity Elements"
The following 39 pages are in this category, out of 39 total.
- Identities are Idempotent
- Identities of Boolean Algebra are also Zeroes
- Identity Element for Power Structure
- Identity is Only Group Element of Order 1
- 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 Subgroup
- Identity of Submagma containing Identity of Magma is Same Identity
- Identity of Subsemigroup of Group
- Identity Property in Semigroup
- Induced Structure Identity
- Inverse of Identity Element is Itself