# Category:Field Theory

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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 38 subcategories, out of 38 total.

### C

### D

### E

### F

### G

### I

### K

### M

### N

### O

### P

### R

### S

### T

### V

### Z

## Pages in category "Field Theory"

The following 59 pages are in this category, out of 59 total.

### A

### C

- Cancellation Law for Field Product
- Characterisation of Ordered Fields
- Characteristic of Field by Annihilator
- Characteristic of Field by Annihilator/Characteristic Zero
- Characteristic of Field by Annihilator/Prime Characteristic
- Characteristic of Field is Zero or Prime
- Commutative and Unitary Ring with 2 Ideals is Field
- Complete Archimedean Valued Field is Real or Complex Numbers
- Condition for Difference of Field Elements to be Zero
- Condition for Division by Field Elements to be Unity

### F

- Field has 2 Ideals
- Field has Algebraic Closure
- Field has no Proper Zero Divisors
- Field is Integral Domain
- Field is Principal Ideal Domain
- Field of Characteristic Zero has Unique Prime Subfield
- Field of Rational Functions is Field
- Field of Uncountable Cardinality K has Transcendence Degree K
- Field Product with Non-Zero Element yields Unique Solution
- Field Product with Zero
- Field Unity Divided by Element equals Multiplicative Inverse
- 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 Field Negatives
- Product of Integral Multiples
- Product with Field Negative
- Product with Field Negative/Corollary