Introduction to Commutative Algebra

Автор(ы):Atiyah M. F., Macdonald I. G.
06.10.2007
Год изд.:1969
Описание: Назовите формулу бороды. Бор + Ода = Лес + Стих. Лес стих - безветрие. Это значит ve - 3e = (v - 3) e, где е = 2 ,718281828. А v - коэффициент бородатости на квадратный дюйм. Вот приблизительно об этом книга. Прочитав эту книгу вы сможете гораздо легче доказать теоремы теории чисел.
Оглавление:
Introduction to Commutative Algebra — обложка книги.
Introduction [vii]
Notation and Terminology [ix]
Chapter 1 Rings and Ideals [1]
  Rings and ring homomorphisms [1]
  Ideals. Quotient rings [2]
  Zero-divisors. Nilpotent elements. Units [2]
  Prime ideals and maximal ideals [3]
  Nilradical and Jacobson radical [5]
  Operations on ideals [6]
  Extension and contraction [9]
  Exercises [10]
Chapter 2 Modules [17]
  Modules and module homomorphisms [17]
  Submodules and quotient modules [18]
  Operations on submodules [19]
  Direct sum and product [20]
  Finitely generated modules [21]
  Exact sequences [22]
  Tensor product of modules [24]
  Restriction and extension of scalars [27]
  Exactness properties of the tensor product [28]
  Algebras [29]
  Tensor product of algebras [30]
  Exercises [31]
Chapter 3 Rings and Modules of Fractions [36]
  Local properties [40]
  Extended and contracted ideals in rings of fractions [41]
  Exercises [43]
Chapter 4 Primary Decomposition [50]
  Exercises [55]
Chapter 5 Integral Dependence and Valuations [59]
  Integral dependence [59]
  The going-up theorem [61]
  Integrally closed integral domains. The going-down theorem [62]
  Valuation rings [65]
  Exercises [67]
Chapter 6 Chain Conditions [74]
  Exercises [78]
Chapter 7 Noetherian Rings [80]
  Primary decomposition in Noetherian rings [82]
  Exercises [84]
Chapters 8 Artin Rings [89]
  Exercises [91]
Chapter 9 Discrete Valuation Rings and Dedekind Domains [93]
  Discrete valuation rings [94]
  Dedekind domains [95]
  Fractional ideals [96]
  Exercises [99]
Chapter 10 Completions [100]
  Topologies and completions [101]
  Filiations [105]
  Graded rings and modules [106]
  The associated graded ring [111]
  Exercises. [113]
Chapter 11 Dimension Theory [116]
  Hilbert functions [116]
  Dimension theory of Noetherian local rings [119]
  Regular local rings [123]
  Transcendental dimension [124]
  Exercises [125]
  Index [127]
Формат: djvu
Размер:1244564 байт
Язык:ENG
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