# Category:Field Theory

This category contains results about Field Theory.

Definitions specific to this category can be found in Definitions/Field Theory.

**Field Theory** is a branch of abstract algebra which studies fields and other related algebraic structures.

## Subcategories

This category has the following 31 subcategories, out of 31 total.

### C

### D

### E

### F

### G

### K

### M

### O

### P

### Q

### R

### S

### T

### V

## Pages in category "Field Theory"

The following 44 pages are in this category, out of 44 total.

### A

### C

### F

- Field has 2 Ideals
- Field has Algebraic Closure
- Field has no Proper Zero Divisors
- Field is Integral Domain
- Field of Characteristic Zero has Unique Prime Subfield
- Field of Rational Functions is Field
- Field of Uncountable Cardinality K has Transcendence Degree K
- Finite Multiplicative Subgroup of Field is Cyclic
- Finite Ring with Multiplicative Norm is Field
- Finite Ring with No Proper Zero Divisors is Field
- Frobenius Endomorphism on Field is Injective

### I

### M

### N

### P

- Polynomial Forms over Field form Integral Domain/Formulation 1
- Polynomial Forms over Field form Principal Ideal Domain
- Polynomial Forms over Field is Euclidean Domain
- Power Function is Completely Multiplicative
- Power to Characteristic of Field is Monomorphism
- Power to Characteristic Power of Field is Monomorphism
- Product of Integral Multiples