A01=Kaiming Zhao
Algebraic Closure
Author_Kaiming Zhao
Category=PBF
Cohen-Macaulay Ring
CohenAcAEURA"Macaulay Ring
Cohn's Criterion
Cyclotomic Polynomials
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euclidean Domain
Field
Field Extensions
Field of Quotients of an Integral Domain
Finite Fields
Finite Normal Extension Field
Finitely Generated Modules Over Euclidean Domains
Gaussian Integers
Isomorphism Theorems
Lindemann-Weierstrass Theorem
LindemannAcAEURA"Weierstrass Theorem
Luroth's Theorem
Maximal Ideal
Noetherian Rings
Osada's Criterion
Perfect Field
Perron's Criterion
Polynomial Rings Over Unique Factorization Domains
Prime Ideal
Principal Ideal Domain
Quotient Ring
Ring
SchAfA?nemannAcAEURA"Eisenstein Criterion
Schonemann-Eisenstein Criterion
Separable Extension Field
Smith Normal Form of Matrices Over Euclidean Domains
Solvability by Radicals
Splitting Extension Field
The Fundamental Theorem of Algebra
The Fundamental Theorem of Galois Theory
Unique Factorization Domain
Product details
- ISBN 9789811255779
- Publication Date: 17 May 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
This book is intended as a textbook for a one-term senior undergraduate (or graduate) course in Ring and Field Theory, or Galois theory. The book is ready for an instructor to pick up to teach without making any preparations.The book is written in a way that is easy to understand, simple and concise with simple historic remarks to show the beauty of algebraic results and algebraic methods. The book contains 240 carefully selected exercise questions of varying difficulty which will allow students to practice their own computational and proof-writing skills. Sample solutions to some exercise questions are provided, from which students can learn to approach and write their own solutions and proofs. Besides standard ones, some of the exercises are new and very interesting. The book contains several simple-to-use irreducibility criteria for rational polynomials which are not in any such textbook.This book can also serve as a reference for professional mathematicians. In particular, it will be a nice book for PhD students to prepare their qualification exams.
