Algebra

Field Theory : Motivation and Basics

Field Theory : Definition of Field

Field Theory : Field of Rationals, Reals and Complex numbers

Field Theory : Example of a field

Field Theory : Integer modulus p (p is prime) is a field.

Field Theory : What is a Subfield?

Field Theory : Results on Subfield

Field Theory : Finite field and its examples

Field Theory : Characteristic of a field

Field Theory : ch(F) is either 0 or a prime number

Field Theory : What is a prime subfield?

Field Theory : Order of a finite field

Field Theory : Revisiting polynomials

Field Theory : It all starts with polynomials!

Field Theory : Order of a subfield of a finite field

Field Theory : Reducibility tests for polynomials of degree 2 or 3

Field Theory : Irreducibility tests for polynomials

Field Theory : Eisentein's Criterion

#19 Field Theory : Cyclotomic polynomials

#20 Field Theory : Connection between irreducible polynomials and Field

#21 Field Theory : What is a field extension?

#22 Field Theory : Finite extension of a finite extension is a finite extension

#23 Field Theory : Embedding of a field F into a field E implies E is an extension of F

#24 Field Theory : Kronecker Theorem (Existence of extension)

#25 Field Theory : How to create an extension field by adjoining an element?

#26 Field Theory : Algebraic and Transcendental Field Extensions

#27 Field Theory : Every finite extension is an algebraic extension

#28 Field Theory : Not every Algebraic extension is a field extension