Category:Cancellability
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This category contains results about cancellable elements.
Definitions specific to this category can be found in Definitions/Cancellability.
Let $\struct {S, \circ}$ be an algebraic structure.
An element $x \in \struct {S, \circ}$ is cancellable if and only if:
- $\forall a, b \in S: x \circ a = x \circ b \implies a = b$
- $\forall a, b \in S: a \circ x = b \circ x \implies a = b$
Subcategories
This category has the following 8 subcategories, out of 8 total.
Pages in category "Cancellability"
The following 31 pages are in this category, out of 31 total.
C
- Cancellable Element is Cancellable in Subset
- Cancellable Elements of Semigroup form Subsemigroup
- Cancellable Finite Semigroup is Group
- Cancellable iff Regular Representations Injective
- Cancellable Infinite Semigroup is not necessarily Group
- Cancellation Laws
- Condition for Invertibility in Power Structure on Associative or Cancellable Operation
I
L
- Left Cancellable Commutative Operation is Right Cancellable
- Left Cancellable Elements of Semigroup form Subsemigroup
- Left Cancellable iff Left Regular Representation Injective
- Left Regular Representation wrt Left Cancellable Element on Finite Semigroup is Bijection
- Lexicographically Ordered Pair of Ordered Semigroups with Cancellable Elements
O
P
R
- Reflexive Reduction of Relation Compatible with Cancellable Operation is Compatible
- Regular Representation wrt Cancellable Element on Finite Semigroup is Bijection
- Right Cancellable Commutative Operation is Left Cancellable
- Right Cancellable Elements of Semigroup form Subsemigroup
- Right Cancellable iff Right Regular Representation Injective
- Right Regular Representation wrt Right Cancellable Element on Finite Semigroup is Bijection