# Category:Isomorphisms (Abstract Algebra)

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This category contains results about **isomorphisms** in the context of **abstract algebra**.

Definitions specific to this category can be found in Definitions/Isomorphisms (Abstract Algebra).

An **isomorphism** is a homomorphism which is a bijection.

That is, it is a mapping which is both a monomorphism and an epimorphism.

## Subcategories

This category has the following 26 subcategories, out of 26 total.

### A

### E

- Embedding Theorem (3 P)

### F

### G

### I

- Isomorphism Preserves Groups (3 P)

### M

- Module Isomorphisms (1 P)
- Monoid Isomorphisms (empty)

### R

### S

### T

- Transplanting Theorem (2 P)

## Pages in category "Isomorphisms (Abstract Algebra)"

The following 30 pages are in this category, out of 30 total.

### C

- Composite of Isomorphisms in Algebraic Structure is Isomorphism
- Composite of Isomorphisms is Isomorphism
- Composite of Isomorphisms is Isomorphism/Algebraic Structure
- Composite of Isomorphisms is Isomorphism/R-Algebraic Structure
- Condition for Isomorphism between Structures Induced by Permutations
- Construction of Inverse Completion/Quotient Mapping to Image is Isomorphism

### I

- Induced Structure from Doubleton is Isomorphic to External Direct Product with Self
- Inverse of Algebraic Structure Isomorphism is Isomorphism
- Isomorphism between Algebraic Structures induces Isomorphism between Induced Structures
- Isomorphism by Cayley Table
- Isomorphism is Equivalence Relation
- Isomorphism of External Direct Products
- Isomorphism Preserves Associativity
- Isomorphism Preserves Cancellability
- Isomorphism Preserves Commutativity
- Isomorphism Preserves Groups
- Isomorphism Preserves Identity
- Isomorphism Preserves Inverses
- Isomorphism Preserves Semigroups
- Isomorphism Theorems