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: 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 + ocr Размер: 7762902 байт Язык: ENG Рейтинг: 57
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