000 04971nam a22004935i 4500
001 978-1-4612-6101-8
003 DE-He213
005 20210921163821.0
007 cr nn 008mamaa
008 121227s1974 xxu| s |||| 0|eng d
020 _a9781461261018
_9978-1-4612-6101-8
024 7 _a10.1007/978-1-4612-6101-8
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aHungerford, Thomas W.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAlgebra
_h[electronic resource] /
_cby Thomas W. Hungerford.
250 _a1st ed. 1974.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1974.
300 _aXXIV, 504 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v73
505 0 _aIntroduction: Prerequisites and Preliminaries -- 1. Logic -- 2. Sets and Classes -- 3. Functions -- 4. Relations and Partitions -- 5. Products -- 6. The Integers -- 7. The Axiom of Choice, Order and Zorn's Lemma -- 8. Cardinal Numbers -- I: Groups -- 1. Semigroups, Monoids and Groups -- 2. Homomorphisms and Subgroups -- 3. Cyclic Groups -- 4. Cosets and Counting -- 5. Normality, Quotient Groups, and Homomorphisms -- 6. Symmetric, Alternating, and Dihedral Groups -- 7. Categories: Products, Coproducts, and Free Objects -- 8. Direct Products and Direct Sums -- 9. Free Groups, Free Products, Generators & Relations -- II: The Structure of Groups -- 1. Free Abelian Groups -- 2. Finitely Generated Abelian Groups -- 3. The Kruli-Schmidt Theorem -- 4. The Action of a Group on a Set -- 5. The Sylow Theorems -- 6. Classification of Finite Groups -- 7. Nilpotent and Solvable Groups -- 8. Normal and Subnormal Series -- III: Rings -- 1. Rings and Homomorphisms -- 2. Ideals -- 3. Factorization in Commutative Rings -- 4. Rings of Quotients and Localization -- 5. Rings of Polynomials and Formal Power Series -- 6. Factorization in Polynomial Rings -- IV: Modules -- 1. Modules, Homomorphisms and Exact Sequences -- 2. Free Modules and Vector Spaces -- 3. Projective and Injective Modules -- 4. Horn and Duality -- 5. Tensor Products -- 6. Modules over a Principal Ideal Domain -- 7. Algebras -- V: Fields and Galois Theory -- 1. Field Extensions -- 2. The Fundamental Theorem -- 3. Splitting Fields, Algebraic Closure and Normality -- 4. The Galois Group of a Polynomial -- 5. Finite Fields -- 6. Separability -- 7. Cyclic Extensions -- 8. Cyclotomic Extensions -- 9. Radical Extensions -- VI: The Structure of Fields -- 1. Transcendence Bases -- 2. Linear Disjointness and Separability -- VII: Linear Algebra -- 1. Matrices and Maps -- 2. Rank and Equivalence -- 3. Determinants -- 4. Decomposition of a Single Linear Transformation and Similarity -- 5. The Characteristic Polynomial, Eigenvectors and Eigenvalues -- VIII: Commutative Rings and Modules -- 1. Chain Conditions -- 2. Prime and Primary Ideals -- 3. Primary Decomposition -- 4. Noetherian Rings and Modules -- 5. Ring Extensions -- 6. Dedekind Domains -- 7. The Hilbert Nullstellensatz -- IX: The Structure of Rings -- 1. Simple and Primitive Rings -- 2. The Jacobson Radical -- 3. Semisimple Rings -- 4. The Prime Radical; Prime and Semiprime Rings -- 5. Algebras -- 6. Division Algebras -- X: Categories -- 1. Functors and Natural Transformations -- 2. Adjoint Functors -- 3. Morphisms -- List of Symbols.
520 _aAlgebra 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.
650 0 _aAlgebra.
650 1 4 _aAlgebra.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11000
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9781461261032
776 0 8 _iPrinted edition:
_z9780387905181
776 0 8 _iPrinted edition:
_z9781461261025
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v73
856 4 0 _uhttps://doi.org/10.1007/978-1-4612-6101-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-BAE
999 _c9526
_d9526