Abstract Algebra, Lec 31B: Z[sqrt(-5)] is not a UFD, Exam 3 Review: (Mostly) Ring Theory

preview_player
Показать описание

Abstract Algebra, Lecture 31B.

(0:00) Idea of the proof that 21 does not factor uniquely as a product of irreducibles in Z[sqrt(-5)] (so Z[sqrt(-5)] is an ID (integral domain) which is not a UFD (unique factorization domain).
(10:15) Review Gallian Chapters 10 & 11 (Group homomorphisms, Fundamental Theorem of Finite Abelian Groups (compute the number of partitions of 6 and 5).
(18:57) Review Gallian Chapters 12 & 13 (Rings, Integral Domains, and Fields).
(23:29) Review Gallian Chapters 14 & 15 (Ideals, Factor Rings, Ring Homomorphisms).
(27:49) Review Gallian Chapters 16 & 17 (Polynomial Rings & Factorization).

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.
  1. Bill Kinney
  2. modern algebra
  3. ring theory
  4. group theory
  5. field theory
  6. integral domain
Рекомендации по теме
Abstract Algebra, Lec 0:30:19

Abstract Algebra, Lec 31B: Z[sqrt(-5)] is not a UFD, Exam 3 Review: (Mostly) Ring Theory

Abstract Alg, Lec 0:36:34

Abstract Alg, Lec 31A: Review Special Integral Domains: UFDs, PIDs, EDs (also Irreducibles, Primes)

Decide whether z(sqrt(-5)) 0:01:08

Decide whether z(sqrt(-5)) unique factorization domain or not (ring theory) | Plainmath

Abstract Algebra, 30B: 0:27:01

Abstract Algebra, 30B: Integral Domains: Irreducibles, Primes, PIDs, UFDs, Fermat's Last Thm, E...

Irreducible and Prime 0:26:27

Irreducible and Prime Elements | Modern Algebra

Abstract Algebra 16.2: 0:11:15

Abstract Algebra 16.2: Associates, Irreducibles, Primes

An Irreducible Element 0:08:04

An Irreducible Element that is Not a Prime

Group Theory 91, 0:09:53

Group Theory 91, Euclidean Domain implies Unique factorization Domain

Abstract Algebra | 0:36:49

Abstract Algebra | A PID that is not a Euclidean Domain

Abstract Algebra | 0:25:43

Abstract Algebra | If D is a UFD then D[x] is a UFD.

Group Theory 74, 0:08:35

Group Theory 74, Factorization over Integral Domains

iNT 12 04 0:04:44

iNT 12 04 Invertible Elements of the Ring ℤ√a and Pell's equations

Abstract Algebra: Euclidean 0:47:40

Abstract Algebra: Euclidean Domains, UFD begins, 11-5-18

Group Theory 85, 0:12:24

Group Theory 85, Irreducible but not a prime

82 Examples of 0:12:24

82 Examples of integral domains

Another Unique Factorization 0:12:55

Another Unique Factorization Fail

Units of Z[√2] 0:09:53

Units of Z[√2] is infinite set | units of Z[√-5] is finite set | Proof using norm| Ring

Commutative algebra 9 0:25:55

Commutative algebra 9 (Euclidean domains)

Unique Factorization Domain 0:13:31

Unique Factorization Domain is Integrally Closed

Abstract Algebra 14.3: 0:08:08

Abstract Algebra 14.3: Subring Theorems

Euclidean Domains are 0:14:09

Euclidean Domains are PIDs (Algebra 2: Lecture 3 Video 5)

Rapid Review of 0:13:16

Rapid Review of Factorization in Integral Domains: Euclidean Domains, PID, UFD & Noetherian Dom...

Ring Theory-Units of 0:02:02

Ring Theory-Units of polynomial Ring

Abstract Algebra: ED 0:51:13

Abstract Algebra: ED implies PID implies UFD, some number theory, 11-29-17

Комментарии
Автор

thank you for the explanation. Please teacher, could you help me with this following exercise? show that Z[ √ 5] ≃ Z[X]/(x^2 − 5) not is a field

lucasolimpio
Автор

Check that (29, 13+√-5) is principal ideal of Z[√-5]

muhammadyawar
Автор

Prove that if R and S are nonzero rings then R x S is never a field.
Plz prove it

abeeraansari