Category:Inverse Elements
Jump to navigation
Jump to search
This category contains results about Inverse Elements in the context of Abstract Algebra.
Definitions specific to this category can be found in Definitions/Inverse Elements.
The element $y$ is an inverse of $x$ if and only if:
- $y \circ x = e_S = x \circ y$
that is, if and only if $y$ is both:
- a left inverse of $x$
and:
- a right inverse of $x$.
Subcategories
This category has the following 12 subcategories, out of 12 total.
E
G
I
- Inverse in Group is Unique (4 P)
- Inverse of Group Inverse (4 P)
- Inverse of Group Product (7 P)
S
- Self-Inverse Elements (3 P)
Pages in category "Inverse Elements"
The following 38 pages are in this category, out of 38 total.
C
- Commutation of Inverses in Monoid
- Commutation with Inverse in Monoid
- Commutator of Group Element with Identity is Identity
- Condition for Invertibility in Power Structure on Associative or Cancellable Operation
- Condition for Partition between Invertible and Non-Invertible Elements to induce Congruence Relation on Monoid
E
I
- Inverse Element is Power of Order Less 1
- Inverse in Group is Unique
- Inverse in Monoid is Unique
- Inverse not always Unique for Non-Associative Operation
- Inverse of Field Product
- Inverse of Group Commutator
- Inverse of Group Inverse
- Inverse of Group Product
- Inverse of Identity Element is Itself
- Inverse of Inverse
- Inverse of Inverse in General Algebraic Structure
- Inverse of Inverse in Monoid
- Inverse of Inverse/General Algebraic Structure
- Inverse of Inverse/Monoid
- Inverse of Product
- Inverse of Product in Associative Structure
- Inverse of Product in Monoid
- Inverse of Product/Monoid
- Inverse of Product/Monoid/General Result
- Invertible Element containing Identity in Power Structure
- Invertible Element of Associative Structure is Cancellable
- Invertible Elements of Monoid form Subgroup
- Isomorphism Preserves Inverses