# Category:Cancellability

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This category contains results about cancellable elements.

Let $\left ({S, \circ}\right)$ be an algebraic structure.

An element $x \in \left ({S, \circ}\right)$ is **cancellable** if and only if:

- $\forall a, b \in S: x \circ a = x \circ b \implies a = b$
- $\forall a, b \in S: a \circ x = b \circ x \implies a = b$

... that is, it is both left cancellable and right cancellable.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### C

### I

### S

## Pages in category "Cancellability"

The following 22 pages are in this category, out of 22 total.

### C

### I

- Identity is only Idempotent Cancellable Element
- Identity of Cancellable Monoid is Identity of Submonoid
- Injection iff Left Cancellable
- Invertible Element of Associative Structure is Cancellable
- Invertible Element of Monoid is Cancellable
- Invertible Elements of Monoid form Subgroup of Cancellable Elements
- Isomorphism Preserves Cancellability
- Isomorphism Preserves Left Cancellability
- Isomorphism Preserves Right Cancellability