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Introduction to Modern Algebra and Its Applications. (Record no. 27311)

MARC details
000 -LEADER
fixed length control field 05839nam a22004453i 4500
001 - CONTROL NUMBER
control field EBC6635858
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724115131.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2020 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781000209471
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780367820916
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC6635858
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL6635858
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1255226361
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA162 .G833 2021
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.02
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Gubareni, Nadiya.
245 10 - TITLE STATEMENT
Title Introduction to Modern Algebra and Its Applications.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Milton :
Name of producer, publisher, distributor, manufacturer Taylor & Francis Group,
Date of production, publication, distribution, manufacture, or copyright notice 2020.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2021.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (395 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title Page -- Copyright Page -- Preface -- Contents -- 1. Elements of Number Theory -- 1.1 Divisibility of Integers. Division with Remainder -- 1.2 The Greatest Common Divisor. The Euclidean Algorithm -- 1.3 The Extended Euclidean Algorithm -- 1.4 Relatively Primes -- 1.5 Linear Diophantine Equations -- 1.6 Congruences and their Properties -- 1.7 Linear Congruences -- 1.8 Exercises -- References -- 2. Elements of Group Theory -- 2.1 Semigroups, Monoids and Groups -- 2.2 Subgroups. Cyclic Groups -- 2.3 Permutation Groups -- 2.4 Cosets. Lagrange's Theorem -- 2.5 Normal Subgroups and Quotient Groups -- 2.6 Group Homomorphisms -- 2.7 The Isomorphism Theorems -- 2.8 Exercises -- References -- 3. Examples of Groups -- 3.1 Cycle Notation and Cycle Decomposition of Permutations -- 3.2 Inversions, Parity and Order of a Permutation -- 3.3 Alternating Group -- 3.4 Cyclic Groups -- 3.5 Groups of Symmetries. The Dihedral Groups -- 3.6 Direct Product of Groups -- 3.7 Finite Abelian Groups -- 3.8 Exercises -- References -- 4. Elements of Ring Theory -- 4.1 Rings and Subrings -- 4.2 Integral Domains and Fields -- 4.3 Ideals and Ring Homomorphisms -- 4.4 Quotient Rings -- 4.5 Maximal Ideals. Prime Ideals -- 4.6 Principal Ideal Rings -- 4.7 Euclidean Domains. Euclidean Algorithm -- 4.8 Unique Factorization Domains -- 4.9 Chinese Remainder Theorem -- 4.10 Exercises -- References -- 5. Polynomial Rings in One Variable -- 5.1 Basic Definitions and Properties -- 5.2 Division with Remainder -- 5.3 Greatest Common Divisor of Polynomials -- 5.4 Factorization of Polynomials. Irreducible Polynomials -- 5.5 Roots of Polynomials -- 5.6 Polynomials over Rational Numbers -- 5.7 Quotient Rings of Polynomial Rings -- 5.8 Exercises -- References -- 6. Elements of Field Theory -- 6.1 A Field of Fractions of an Integral Domain -- 6.2 The Characteristic of a Field.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 6.3 Field Extensions -- 6.4 Algebraic Elements. Algebraic Extensions -- 6.5 Splitting Fields -- 6.6 Algebraically Closed Fields -- 6.7 Polynomials over Complex Numbers and Real Numbers -- 6.8 Exercises -- References -- 7. Examples of Applications -- 7.1 Euler's φ-function and its Properties -- 7.2 Euler's Theorem. Fermat's Little Theorem. Wilson's Theorem -- 7.3 Solving Linear Congruences by Euler's Method -- 7.4 Solving Systems of Linear Congruences -- 7.5 Lagrange's Interpolation Polynomials -- 7.6 Secret Sharing -- 7.7 Cryptographic Algorithm RSA -- 7.8 Exercises -- References -- 8. Polynomials in Several Variables -- 8.1 Polynomial Rings in Several Variables -- 8.2 Symmetric Polynomials -- 8.3 Noetherian Rings. Hilbert Basis Theorem -- 8.4 Monomial Order -- 8.5 Division Algorithm for Polynomials -- 8.6 Initial Ideals. Gröbner Basis -- 8.7 S-polynomials -- 8.8 Buchberger's Algorithm -- 8.9 Minimal and Reduced Gröbner Basis -- 8.10 Applications of Gröbner Bases -- 8.11 Exercises -- References -- 9. Finite Fields and their Applications -- 9.1 Properties of Finite Fields -- 9.2 Multiplicative Group of a Finite Field -- 9.3 Primitive Roots and Indexes. Discrete Logarithm Problem -- 9.4 Diffie-Hellman Scheme. ElGamal Cryptosystem -- 9.5 Error Detecting and Error Correcting Codes -- 9.6 Exercises -- References -- 10. Finite Dimensional Algebras -- 10.1 Quaternions and their Properties -- 10.2 Octonions-Cayley's Octaves -- 10.3 Algebras and their Properties -- 10.4 Division Algebras. Algebras with Involution. Composition Algebras -- 10.5 Cayley-Dickson Construction -- 10.6 Dual Numbers and Double Numbers -- 10.7 Clifford Algebras. Grassmann Algebras -- 10.8 Exercises -- References -- 11. Applications of Quaternions and Octonions -- 11.1 Square Sum Identities -- 11.2 Gaussian Integers -- 11.3 Fermat's Theorem on Sums of Two Squares.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 11.4 Lagrange's Four-Square Theorem -- 11.5 Trigonometric Form of Quaternions -- 11.6 Rotations and Quaternions -- 11.7 Exercises -- References -- Appendix -- A.1 Basic Concepts of Set Theory. Relations on Sets -- A.2 Operations on Sets. Algebraic Structures -- A.3 Vector Spaces -- Index.
520 ## - SUMMARY, ETC.
Summary, etc. The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Algebra, Abstract-Textbooks.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Gubareni, Nadiya
Title Introduction to Modern Algebra and Its Applications
Place, publisher, and date of publication Milton : Taylor & Francis Group,c2020
International Standard Book Number 9780367820916
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6635858">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6635858</a>
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