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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 $x$
- a right inverse of $x$.
This category has the following 11 subcategories, out of 11 total.
- Self-Inverse Elements (3 P)
Pages in category "Inverse Elements"
The following 34 pages are in this category, out of 34 total.
- 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 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