# 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 9 subcategories, out of 9 total.

### E

### F

### G

### I

### M

### S

## Pages in category "Monoids"

The following 49 pages are in this category, out of 49 total.

### C

### F

### I

- Idempotent Elements form Submonoid of Commutative Monoid
- Identity of Cancellable Monoid is Identity of Submonoid
- 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 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 Set of Monoid under Induced Operation is Monoid
- Powers of Commutative Elements in Monoids
- Powers of Commuting Elements of Monoid Commute
- Product of Commuting Elements with Inverses