Algebra

Front Cover
Springer Science & Business Media, 1974 - Mathematics - 502 pages
9 Reviews
Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.
  

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Review: Algebra (Graduate Texts in Mathematics) (Graduate Texts in Mathematics #73)

User Review  - Sara - Goodreads

Great all-purpose graduate reference book. Highly recommended. Read full review

Review: Algebra (Graduate Texts in Mathematics) (Graduate Texts in Mathematics #73)

User Review  - Han Zhicheng - Goodreads

The first-ever GTM text in my life. Hopefully this will kick a good start. This book is excellent for those beginner in algebra who would like to have a panorama of this field. Its settings are clear ... Read full review

Contents

Groups
23
1 Semigroups Monoids and Groups
24
2 Homomorphisms and Subgroups
30
3 Cyclic Groups
35
4 Cosets and Counting
37
5 Normality Quotient Groups and Homomorphisms
41
6 Symmetric Alternating and Dihedral Groups
46
Products Coproducts and Free Objects
52
4 The Galois Group of a Polynomial
269
5 Finite Fields
278
6 Separability
282
7 Cyclic Extensions
289
8 Cyclotomic Extensions
297
9 Radical Extensions
302
The Structure of Fields
311
2 Linear Disjointness and Separability
318

8 Direct Products and Direct Sums
59
9 Free Groups Free Products Generators Relations
64
The Structure of Groups
70
2 Finitely Generated Abelian Groups
76
3 The KrullSchmidt Theorem
83
4 The Action of a Group on a Set
88
5 The Sylow Theorems
92
6 Classification of Finite Groups
96
7 Nilpotent and Solvable Groups
100
8 Normal and Subnormal Series
107
Rings
114
1 Rings and Homomorphisms
115
2 Ideals
122
3 Factorization in Commutative Rings
135
4 Rings of Quotients and Localization
142
5 Ring of Polynomials and Formal Power Series
149
6 Factorization in Polynomial Rings
157
Modules
168
1 Modules Homomorphisms and Exact Sequences
169
2 Free Modules and Vector Spaces
180
3 Projective and Injective Modules
190
4 Hom and Duality
199
5 Tensor Products
207
6 Modules Over a Principal Ideal Domain
218
7 Algebras
226
Fields and Galois Theory
230
1 Field Extensions
231
2 The Fundamental Theorem
243
3 Splitting Fields Algebraic Closure and Normality
257
Linear Algebra
327
1 Matrices and Maps
328
2 Rank and Equivalence
335
3 Determinants
348
4 Decomposition of a Single Linear Transformation and Similarity
355
5 The Characteristic Polynomial Eigenvectors and Eigenvalues
366
Commutative Rings and Modules
371
1 Chain Conditions
372
2 Prime and Primary Ideals
377
3 Primary Decomposition
383
4 Noetherian Rings and Modules
387
5 Ring Extensions
394
6 Dedekind Domains
400
7 The Hilbert Nullstellensatz
409
The Structure of Rings
414
1 Simple and Primitive Rings
415
2 The Jacobson Radical
424
3 Semisimple Rings
434
4 The Prime Radical Prime and Semiprime Rings
444
5 Algebras
450
6 Division Algebras
456
Categories
464
1 Functors and Natural Transformations
465
2 Adjoint Functors
476
3 Morphisms
480
List of Symbols
485
Bibliography
489
Index
493
Copyright

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About the author (1974)

Thomas W. Hungerford received his M.S. and Ph.D. from the University of Chicago. He has taught at the University of Washington and at Cleveland State University, and is now at St. Louis University. His research fields are algebra and mathematics education. He is the author of many notable books for undergraduate and graduate level courses. In addition to ABSTRACT ALGEBRA: AN INTRODUCTION, these include: ALGEBRA (Springer, Graduate Texts in Mathematics, #73. 1974); MATHEMATICS WITH APPLICATIONS, Tenth Edition (Pearson, 2011; with M. Lial and J. Holcomb); and CONTEMPORARY PRECALCULUS, Fifth Edition (Cengage, 2009; with D. Shaw).

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