# Category:Monoids

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This category contains results about **Monoids**.

Definitions specific to this category can be found in Definitions/Monoids.

A **monoid** is a semigroup with an identity element.

## Subcategories

This category has the following 12 subcategories, out of 12 total.

### C

### E

### F

- Free Monoids (2 P)

### G

### I

- Inverse of Commuting Pair (3 P)

### M

- Monoid Homomorphisms (1 P)

### S

- Submonoids (4 P)

## Pages in category "Monoids"

The following 50 pages are in this category, out of 50 total.

### C

- Cancellable Elements of Monoid form Submonoid
- Commutation of Inverses in Monoid
- Commutation with Inverse in Monoid
- Commutativity of Powers in Monoid
- Condition for Cosets of Subgroup of Monoid to be Partition
- Condition for Partition between Invertible and Non-Invertible Elements to induce Congruence Relation on Monoid
- Condition for Subgroup of Monoid to be Normal
- Conjugate of Commuting Elements

### F

### I

- Identity of Monoid is Cancellable
- Identity of Monoid is Unique
- Index Laws for Monoid
- Index Laws for Monoid/Product of Indices
- Index Laws for Monoid/Sum of Indices
- Index Laws for Monoids
- Index Laws for Monoids/Negative Index
- Index Laws for Monoids/Product of Indices
- Index Laws for Monoids/Sum of Indices
- Index Laws/Product of Indices/Monoid
- Index Laws/Sum of Indices/Monoid
- Inverse in Monoid is Unique
- Inverse of Commuting Pair
- Inverse of Inverse in Monoid
- Inverse of Inverse/Monoid
- Inverse of Product in Associative Structure
- Inverse of Product in Monoid
- Inverse of Product/Monoid
- Inverse of Product/Monoid/General Result
- Invertible Element of Monoid is Cancellable
- Invertible Elements of Monoid form Subgroup
- Invertible Elements of Monoid form Subgroup of Cancellable Elements

### P

- Power of Identity is Identity
- Power of Product of Commutative Elements in Monoid
- Power of Product of Commuting Elements in Monoid equals Product of Powers
- Power Structure of Monoid is Monoid
- Powers of Commutative Elements in Monoids
- Powers of Commuting Elements of Monoid Commute
- Product of Commuting Elements with Inverses