Item Details

Print View

Classic Algebra

P.M. Cohn
Format
Book
Published
Chichester ; New York : J. Wiley, c2000.
Edition
3rd ed
Language
English
ISBN
047187731X (acid-free paper), 0471877328 (pbk. : acid-free paper)
Contents
  • 1 Sets and mappings
  • 1.1 Need for logic 1
  • 1.2 Sets 8
  • 1.3 Mappings 11
  • 1.4 Equivalence relations 16
  • 1.5 Ordered sets 18
  • 2 Integers and rational numbers
  • 2.1 Integers 21
  • 2.2 Divisibility and factorization in Z 25
  • 2.3 Congruences 29
  • 2.4 Rational numbers and some finite fields 35
  • 3 Groups
  • 3.1 Monoids 40
  • 3.2 Groups; the axioms 43
  • 3.3 Group actions and coset decompositions 48
  • 3.4 Cyclic groups 53
  • 3.5 Permutation groups 56
  • 3.6 Symmetry 60
  • 4 Vector spaces and linear mappings
  • 4.1 Vectors and linear dependence 67
  • 4.2 Linear mappings 71
  • 4.3 Bases and dimension 72
  • 4.4 Direct sums and quotient spaces 77
  • 4.5 Space of linear mappings 82
  • 4.6 Change of basis 89
  • 4.7 Rank 91
  • 4.8 Affine spaces 96
  • 4.9 Category and functor 99
  • 5 Linear equations
  • 5.1 Systems of linear equations 106
  • 5.2 Elementary operations 109
  • 5.3 Linear programming 113
  • 5.4 PAQ-reduction and the inversion of matrices 122
  • 5.5 Block multiplication 124
  • 6 Rings and fields
  • 6.1 Definition and examples 129
  • 6.2 Field of fractions of an integral domain 133
  • 6.3 Characteristic 138
  • 6.4 Polynomials 140
  • 6.5 Factorization 145
  • 6.6 Zeros of polynomials 152
  • 6.7 Factorization of polynomials 156
  • 6.8 Derivatives 159
  • 6.9 Symmetric and alternating functions 167
  • 6.10 Field extensions 172
  • 6.11 Roots of unity 175
  • 6.12 Finite fields 177
  • 7 Determinants
  • 7.1 Definition and basic properties 183
  • 7.2 Expansion of a determinant 191
  • 7.3 Determinantal rank 195
  • 7.4 Resultant 197
  • 8 Quadratic forms
  • 8.1 Bilinear forms and pairings 204
  • 8.2 Dual spaces 207
  • 8.3 Inner products; quadratic and hermitian forms 211
  • 8.4 Euclidean and unitary spaces 219
  • 8.5 Orthogonal and unitary matrices 223
  • 8.6 Alternating forms 235
  • 9 Further group theory
  • 9.1 Isomorphism theorems 242
  • 9.2 Jordan-Holder theorem 247
  • 9.3 Groups with operators 251
  • 9.4 Automorphisms 255
  • 9.5 Derived group; soluble groups and simple groups 258
  • 9.6 Direct products 263
  • 9.7 Abelian groups 270
  • 9.8 Sylow theorems 277
  • 9.9 Generators and defining relations; free groups 282
  • 10 Rings and modules
  • 10.1 Ideals and quotient rings 290
  • 10.2 Modules over a ring 293
  • 10.3 Direct products and direct sums 299
  • 10.4 Free modules 304
  • 10.5 Principal ideal domains 308
  • 10.6 Modules over a principal ideal domain 315
  • 10.7 Linear algebras 321
  • 10.8 Construction of field extensions 323
  • 10.9 Semisimple modules and rings 326
  • 10.10 Radical of a ring 331
  • 10.11 Tensor products of modules and of algebras 335
  • 11 Normal forms for matrices
  • 11.1 Eigenvalues and eigenvectors 341
  • 11.2 K[x]-module defined by an endomorphism 344
  • 11.3 Cyclic endomorphisms 349
  • 11.4 Jordan normal form 352
  • 11.5 Jordan normal form: another method 357
  • 11.6 Normal matrices 360
  • 11.7 Group representatives 362
  • 11.8 Orthnogonality relations and completeness 366
  • 11.9 Characters 371
  • 1 Axiom of choice and Zorn's lemma 377
  • 2 Countable and uncountable sets; transfinite induction 379.
Description
xiv, 428 p. : ill. ; 23 cm.
Notes
  • Rev. ed. of: Algebra. 2nd ed. c1982-c1991.
  • Includes bibliographical references and index.
Technical Details
  • Access in Virgo Classic
  • Staff View

    LEADER 04399pam a2200349 a 4500
    001 u3704688
    003 SIRSI
    005 20001106073519.0
    008 000428s2000 enka b 001 0 eng
    010
      
      
    a| 00033014
    020
      
      
    a| 047187731X (acid-free paper)
    020
      
      
    a| 0471877328 (pbk. : acid-free paper)
    035
      
      
    a| (Sirsi) i047187731X
    035
      
      
    a| (OCoLC)44045580
    040
      
      
    a| DLC c| DLC d| DLC d| MvI
    050
    0
    0
    a| QA154.2 b| .C63 2000
    082
    0
    0
    a| 512.9 2| 21
    090
      
      
    a| MATH/QA154.2 b| .C63 2000
    100
    1
      
    a| Cohn, P. M. q| (Paul Moritz)
    245
    1
    0
    a| Classic algebra / c| P.M. Cohn.
    250
      
      
    a| 3rd ed.
    260
      
      
    a| Chichester ; a| New York : b| J. Wiley, c| c2000.
    300
      
      
    a| xiv, 428 p. : b| ill. ; c| 23 cm.
    500
      
      
    a| Rev. ed. of: Algebra. 2nd ed. c1982-c1991.
    504
      
      
    a| Includes bibliographical references and index.
    505
    0
    0
    g| 1 t| Sets and mappings -- g| 1.1 t| Need for logic g| 1 -- g| 1.2 t| Sets g| 8 -- g| 1.3 t| Mappings g| 11 -- g| 1.4 t| Equivalence relations g| 16 -- g| 1.5 t| Ordered sets g| 18 -- g| 2 t| Integers and rational numbers -- g| 2.1 t| Integers g| 21 -- g| 2.2 t| Divisibility and factorization in Z g| 25 -- g| 2.3 t| Congruences g| 29 -- g| 2.4 t| Rational numbers and some finite fields g| 35 -- g| 3 t| Groups -- g| 3.1 t| Monoids g| 40 -- g| 3.2 t| Groups; the axioms g| 43 -- g| 3.3 t| Group actions and coset decompositions g| 48 -- g| 3.4 t| Cyclic groups g| 53 -- g| 3.5 t| Permutation groups g| 56 -- g| 3.6 t| Symmetry g| 60 -- g| 4 t| Vector spaces and linear mappings -- g| 4.1 t| Vectors and linear dependence g| 67 -- g| 4.2 t| Linear mappings g| 71 -- g| 4.3 t| Bases and dimension g| 72 -- g| 4.4 t| Direct sums and quotient spaces g| 77 -- g| 4.5 t| Space of linear mappings g| 82 -- g| 4.6 t| Change of basis g| 89 -- g| 4.7 t| Rank g| 91 -- g| 4.8 t| Affine spaces g| 96 -- g| 4.9 t| Category and functor g| 99 -- g| 5 t| Linear equations -- g| 5.1 t| Systems of linear equations g| 106 -- g| 5.2 t| Elementary operations g| 109 -- g| 5.3 t| Linear programming g| 113 -- g| 5.4 t| PAQ-reduction and the inversion of matrices g| 122 -- g| 5.5 t| Block multiplication g| 124 -- g| 6 t| Rings and fields -- g| 6.1 t| Definition and examples g| 129 -- g| 6.2 t| Field of fractions of an integral domain g| 133 -- g| 6.3 t| Characteristic g| 138 -- g| 6.4 t| Polynomials g| 140 -- g| 6.5 t| Factorization g| 145 -- g| 6.6 t| Zeros of polynomials g| 152 -- g| 6.7 t| Factorization of polynomials g| 156 -- g| 6.8 t| Derivatives g| 159 -- g| 6.9 t| Symmetric and alternating functions g| 167 -- g| 6.10 t| Field extensions g| 172 -- g| 6.11 t| Roots of unity g| 175 -- g| 6.12 t| Finite fields g| 177 -- g| 7 t| Determinants -- g| 7.1 t| Definition and basic properties g| 183 -- g| 7.2 t| Expansion of a determinant g| 191 -- g| 7.3 t| Determinantal rank g| 195 -- g| 7.4 t| Resultant g| 197 -- g| 8 t| Quadratic forms -- g| 8.1 t| Bilinear forms and pairings g| 204 -- g| 8.2 t| Dual spaces g| 207 -- g| 8.3 t| Inner products; quadratic and hermitian forms g| 211 -- g| 8.4 t| Euclidean and unitary spaces g| 219 -- g| 8.5 t| Orthogonal and unitary matrices g| 223 -- g| 8.6 t| Alternating forms g| 235 -- g| 9 t| Further group theory -- g| 9.1 t| Isomorphism theorems g| 242 -- g| 9.2 t| Jordan-Holder theorem g| 247 -- g| 9.3 t| Groups with operators g| 251 -- g| 9.4 t| Automorphisms g| 255 -- g| 9.5 t| Derived group; soluble groups and simple groups g| 258 -- g| 9.6 t| Direct products g| 263 -- g| 9.7 t| Abelian groups g| 270 -- g| 9.8 t| Sylow theorems g| 277 -- g| 9.9 t| Generators and defining relations; free groups g| 282 -- g| 10 t| Rings and modules -- g| 10.1 t| Ideals and quotient rings g| 290 -- g| 10.2 t| Modules over a ring g| 293 -- g| 10.3 t| Direct products and direct sums g| 299 -- g| 10.4 t| Free modules g| 304 -- g| 10.5 t| Principal ideal domains g| 308 -- g| 10.6 t| Modules over a principal ideal domain g| 315 -- g| 10.7 t| Linear algebras g| 321 -- g| 10.8 t| Construction of field extensions g| 323 -- g| 10.9 t| Semisimple modules and rings g| 326 -- g| 10.10 t| Radical of a ring g| 331 -- g| 10.11 t| Tensor products of modules and of algebras g| 335 -- g| 11 t| Normal forms for matrices -- g| 11.1 t| Eigenvalues and eigenvectors g| 341 -- g| 11.2 t| K[x]-module defined by an endomorphism g| 344 -- g| 11.3 t| Cyclic endomorphisms g| 349 -- g| 11.4 t| Jordan normal form g| 352 -- g| 11.5 t| Jordan normal form: another method g| 357 -- g| 11.6 t| Normal matrices g| 360 -- g| 11.7 t| Group representatives g| 362 -- g| 11.8 t| Orthnogonality relations and completeness g| 366 -- g| 11.9 t| Characters g| 371 -- g| 1 t| Axiom of choice and Zorn's lemma g| 377 -- g| 2 t| Countable and uncountable sets; transfinite induction g| 379.
    596
      
      
    a| 8
    650
      
    0
    a| Algebra.
    700
    1
      
    a| Cohn, P. M. q| (Paul Moritz) t| Algebra.
    999
      
      
    a| QA154.2 .C63 2000 w| LC i| X004474152 l| STACKS m| MATH t| BOOK
▾See more
▴See less

Availability

Google Preview

Google Books Preview
Library Location Map Availability Call Number
Math Stacks N/A Available