RNT1.2.2. Order of a Finite Field

preview_player
Показать описание
Abstract Algebra: Let F be a finite field. Prove that F has p^m elements, where p is prime and m gt 0. We note two approaches: one uses the Fundamental Theorem of Finite Abelian Groups, while the other uses linear algebra.
  1. MathDoctorBob
  2. Mathematics
  3. abstract
  4. algebra
  5. field
  6. theory
Рекомендации по теме
RNT1.2.2. Order of 0:05:47

RNT1.2.2. Order of a Finite Field

Order 2 Elements 0:07:39

Order 2 Elements in Finite Group

RNT1.2.1. Example of 0:07:07

RNT1.2.1. Example of Integral Domain

Order of a 0:02:05

Order of a finite field | finite field of order p #prime field #mathematics #ppsc#math

ORDER OF A 0:06:46

ORDER OF A FINITE FIELD STEP 2

RNT2.1.1. Finite Fields 0:10:37

RNT2.1.1. Finite Fields of Orders 4 and 8

Field Theory: Fields 0:06:26

Field Theory: Fields of Order a Power of a Prime

RNT1.2. Definition of 0:12:55

RNT1.2. Definition of Integral Domain

ORDER OF A 0:06:01

ORDER OF A FINITE FIELD STEP 1

Lecture 2 Part 0:16:36

Lecture 2 Part 4 - Finite Field Z5

FIT1.2. Characteristic p 0:11:25

FIT1.2. Characteristic p

Abstract Algebra 72: 0:08:20

Abstract Algebra 72: The finite field of size p, where p is a prime

Integral Domains (Abstract 0:07:34

Integral Domains (Abstract Algebra)

RNT1.4.1. Example of 0:05:07

RNT1.4.1. Example of Quotient Ring

Tutorial Q2 -- 0:09:40

Tutorial Q2 -- Finite sets closed under addition and addition modulo integer

Group Theory 54, 0:14:53

Group Theory 54, Fields

GT17. Symmetric and 0:20:53

GT17. Symmetric and Alternating Groups

Abstract Algebra 4.2: 0:06:28

Abstract Algebra 4.2: An Order Theorem

Finite fields made 0:08:49

Finite fields made easy

The Field of 0:10:21

The Field of Order 4

Ring Examples (Abstract 0:07:18

Ring Examples (Abstract Algebra)

RT3. Equivalence and 0:19:07

RT3. Equivalence and Examples (Expanded)

302.10C: Constructing Finite 0:15:41

302.10C: Constructing Finite Fields

ALGEBRA AND NUMBER 0:08:31

ALGEBRA AND NUMBER THEORY - FINITE FIELDS AND POLYNOMIALS

Комментарии
Автор

I you have any specific problems that you want to see, let me know. - Bob

MathDoctorBob
Автор

Good morning children. Today you will learn mathematics. Or else...

Thank you for making the video series!

ViatoremDiEfa
Автор

@Nazlijelveh That's step 1: Every finite field has characteristic of prime order q. Since F is a vector space over this prime field, F has order q^m. Since p and q are prime, p=q ad m=n. - Bob

MathDoctorBob
Автор

@Nazlijelveh The only assumption we have is that F is finite. The first step is to show that there is a subfield of prime order (which we call p). Sorry for not being clear. - Bob

MathDoctorBob
Автор

Bob, it is very nice to have this lectures, but are the RNT lectures pack is available as it is available in group theory??

notunkabita
Автор

Two operations: 1) under multiplication, the nonzero elements form a cyclic group, and 2) under addition, F is a direct product of Z/p's, where p is the characteristic. To decompose, 1 generates a Z/p. Then F is a vector space over Z/p, and choosing a basis over Z/p gives the product. - Bob

MathDoctorBob
Автор

Since F is a finite field, then it is a cyclic group (and thus generated by one element). the issue is that i don't get how to make that decomposition: F is product of Z/ni where ni|n(i+1)...

Ramzythemaster
Автор

could you add more lectures on Galois theory ??!!, please

mathWisdom
Автор

yes I want to understand better how to find element of Galois group ( be exactly automorphism)

mathWisdom
Автор

Everything is in the Abstract Algebra playlist in order. I haven't done problems for Ring Theory yet. Maybe in the future.

MathDoctorBob
Автор

@Thatdarnmonkeylove You're welcome! - Bob

MathDoctorBob
Автор

@porkinmycorkhole Admittedly this video is mostly abstract nonsense. To give examples with order p^2 or higher, we need to develop some theory for irreducible polynomials over Z/p. - Bob

MathDoctorBob
Автор

Sounds a bit like the ultimate warrior.

Freddyphelp