Rings and Fields

Hardcover (Print)
Buy New
Buy New from BN.com
$132.01
Used and New from Other Sellers
Used and New from Other Sellers
from $3.09
Usually ships in 1-2 business days
(Save 97%)
Other sellers (Hardcover)
  • All (8) from $3.09   
  • New (2) from $155.88   
  • Used (6) from $3.09   

Overview

This accessible introduction to the mathematics of rings and fields shows how algebraic techniques can be used to solve many difficult problems. The book is carefully organized. Prerequisite mathematical skills are introduced at the beginning, and each chapter opens with an introduction to a problem followed by the development of the algebraic techniques necessary for its solution, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is not required, a chapter is included which states the axiom for a group and proves the group theoretic results needed in Galois theory. The work is intended for advanced students and researchers in mathematics, computer science, and electronic engineering.

Read More Show Less

Product Details

  • ISBN-13: 9780198534556
  • Publisher: Oxford University Press, USA
  • Publication date: 12/28/1992
  • Series: Oxford Science Publications
  • Pages: 184
  • Product dimensions: 9.50 (w) x 6.31 (h) x 0.63 (d)

Meet the Author

University College, Galway
Read More Show Less

Table of Contents

0 Preliminaries 1
Definition of rings and fields
Vector spaces
Bases
Equivalence relations
Axiom of choice
1 Diophantine equations: Euclidean domains 13
Euclidean domain of Gaussian integers
Euclidean domains as unique factorization domains
2 Construction of projective planes: splitting fields and finite fields 25
Existence and uniqueness of splitting fields and of finite fields of prime power order
3 Error codes: primitive elements and subfields 49
Existence of primitive elements in finite fields
Subfields of finite fields
Computation of minimum polynomials
4 Construction of primitive polynomials: cyclotomic polynomials and factorization 65
Basic properties of cyclotomic polynomials
Berlekamp's factorization algorithm
5 Ruler and compass constructions: irreducibility and constructibility 83
Product formula for the degree of composite extensions
Irreducibility criteria for polynomials over the rationals
The field of constructible real numbers
6 Pappus' theorem and Desargues' theorem in projective planes: Wedderburn's theorem 93
Proof of Wedderburn's theorem
7 Solution of polynomials by radicals: Galois groups 109
Basic definitions and results in Galois groups
Discriminants
8 Introduction to groups 135
Group axioms
Subgroup lattice
Class equation
Cauchy's theorem
Transitive permutation groups
Soluble groups
9 Crytography: elliptic curves and factorization 151
Euler's function
Discrete logarithms
Elliptic curves
Pollard's method of factorizing integers
Elliptic curve factorization of integers
Further reading 166
Index 167
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)