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Algebra : an approach via module theory

Algebra : an approach via module theory (4회 대출)

자료유형
단행본
개인저자
Adkins, William A. Weintraub, Steven H.
서명 / 저자사항
Algebra : an approach via module theory / William A. Adkins, Steven H. Weintraub.
발행사항
New York :   Springer-Verlag ,   c1992   (1999 corrected second printing)  
형태사항
x, 526 p. : ill. ; 25 cm.
총서사항
Graduate texts in mathematics ; 136
ISBN
0387978399 3540978399 (Berlin) 9780387978390
서지주기
Includes bibliographical references (p. [510]) and indexes.
일반주제명
Algebra. Modules (Algebra)
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001 000045458907
005 20080804105650
008 920312s1992 nyua b 001 0 eng
010 ▼a 92011951
020 ▼a 0387978399
020 ▼a 3540978399 (Berlin)
020 ▼a 9780387978390
035 ▼a (KERIS)REF000014697328
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA154 ▼b .A33 1992
082 0 0 ▼a 512/.4 ▼2 22
090 ▼a 512.4 ▼b A236a
100 1 ▼a Adkins, William A.
245 1 0 ▼a Algebra : ▼b an approach via module theory / ▼c William A. Adkins, Steven H. Weintraub.
260 ▼a New York : ▼b Springer-Verlag , ▼c c1992 ▼g (1999 corrected second printing)
300 ▼a x, 526 p. : ▼b ill. ; ▼c 25 cm.
440 0 ▼a Graduate texts in mathematics ; ▼v 136
504 ▼a Includes bibliographical references (p. [510]) and indexes.
650 0 ▼a Algebra.
650 0 ▼a Modules (Algebra)
700 1 ▼a Weintraub, Steven H.
945 ▼a KINS

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.4 A236a 등록번호 121174145 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

1 Groups.- 1.1 Definitions and Examples.- 1.2 Subgroups and Cosets.- 1.3 Normal Subgroups, Isomorphism Theorems, and Automorphism Groups.- 1.4 Permutation Representations and the Sylow Theorems.- 1.5 The Symmetric Group and Symmetry Groups.- 1.6 Direct and Semidirect Products.- 1.7 Groups of Low Order.- 1.8 Exercises.- 2 Rings.- 2.1 Definitions and Examples.- 2.2 Ideals, Quotient Rings, and Isomorphism Theorems.- 2.3 Quotient Fields and Localization.- 2.4 Polynomial Rings.- 2.5 Principal Ideal Domains and Euclidean Domains.- 2.6 Unique Factorization Domains.- 2.7 Exercises.- 3 Modules and Vector Spaces.- 3.1 Definitions and Examples.- 3.2 Submodules and Quotient Modules.- 3.3 Direct Sums, Exact Sequences, and Horn.- 3.4 Free Modules.- 3.5 Projective Modules.- 3.6 Free Modules over a PID.- 3.7 Finitely Generated Modules over PIDs.- 3.8 Complemented Submodules.- 3.9 Exercises.- 4 Linear Algebra.- 4.1 Matrix Algebra.- 4.2 Determinants and Linear Equations.- 4.3 Matrix Representation of Homomorphisms.- 4.4 Canonical Form Theory.- 4.5 Computational Examples.- 4.6 Inner Product Spaces and Normal Linear Transformations.- 4.7 Exercises.- 5 Matrices over PIDs.- 5.1 Equivalence and Similarity.- 5.2 Hermite Normal Form.- 5.3 Smith Normal Form.- 5.4 Computational Examples.- 5.5 A Rank Criterion for Similarity.- 5.6 Exercises.- 6 Bilinear and Quadratic Forms.- 6.1 Duality.- 6.2 Bilinear and Sesquilinear Forms.- 6.3 Quadratic Forms.- 6.4 Exercises.- 7 Topics in Module Theory.- 7.1 Simple and Semisimple Rings and Modules.- 7.2 Multilinear Algebra.- 7.3 Exercises.- 8 Group Representations.- 8.1 Examples and General Results.- 8.2 Representations of Abelian Groups.- 8.3 Decomposition of the Regular Representation.- 8.4 Characters.- 8.5 Induced Representations.- 8.6 Permutation Representations.- 8.7 Concluding Remarks.- 8.8 Exercises.- Index of Notation.- Index of Terminology.


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