Algebra II: Chapters 4 - 7Springer Science & Business Media, 16 avr. 2003 - 453 pages This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and based on it is Chapter 7: modules over a p.i.d. studies of torsion modules, free modules, finite type modules, with applications to abelian groups and endomorphisms of vector spaces. Sections on semi-simple endomorphisms and Jordan decomposition have been added. Chapter IV: Polynomials and Rational Fractions Chapter V: Commutative Fields Chapter VI: Ordered Groups and Fields Chapter VII: Modules Over Principal Ideal Domains
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Table des matières
I | A-1 |
II | A-2 |
III | A-4 |
IV | A-6 |
V | A-9 |
VI | A-10 |
VII | A-11 |
VIII | A-13 |
CXVIII | A-94 |
CXIX | A-96 |
CXX | A-97 |
CXXI | A-98 |
CXXIII | A-100 |
CXXIV | A-104 |
CXXV | A-106 |
CXXVI | A-107 |
IX | A-14 |
X | A-17 |
XII | A-19 |
XIII | A-20 |
XIV | A-21 |
XV | A-23 |
XVI | A-24 |
XVII | A-25 |
XVIII | A-28 |
XIX | A-30 |
XX | A-31 |
XXI | A-32 |
XXII | A-35 |
XXIII | A-38 |
XXV | A-39 |
XXVI | A-41 |
XXVII | A-42 |
XXVIII | A-43 |
XXIX | A-45 |
XXX | A-47 |
XXXI | A-48 |
XXXII | A-50 |
XXXIII | A-52 |
XXXIV | A-54 |
XXXV | A-57 |
XXXVI | A-59 |
XXXVII | A-61 |
XXXVIII | A-67 |
XL | A-70 |
XLI | A-72 |
XLII | A-75 |
XLIII | A-81 |
XLIV | A-86 |
XLV | A-87 |
XLVI | A-89 |
XLVII | A-90 |
XLVIII | A-91 |
XLIX | A-98 |
L | A-103 |
LI | A-1 |
LII | A-2 |
LIII | A-3 |
LIV | A-5 |
LV | A-7 |
LVII | A-9 |
LVIII | A-10 |
LX | A-12 |
LXI | A-13 |
LXII | A-15 |
LXIII | A-17 |
LXIV | A-19 |
LXVI | A-21 |
LXVII | A-22 |
LXVIII | A-24 |
LXX | A-25 |
LXXI | A-26 |
LXXIII | A-28 |
LXXV | A-30 |
LXXVI | A-31 |
LXXVII | A-33 |
LXXVIII | A-34 |
LXXIX | A-36 |
LXXX | A-37 |
LXXXI | A-39 |
LXXXII | A-40 |
LXXXIII | A-41 |
LXXXIV | A-42 |
LXXXV | A-43 |
LXXXVI | A-45 |
LXXXVII | A-46 |
LXXXVIII | A-47 |
XCI | A-50 |
XCII | A-52 |
XCV | A-53 |
XCVI | A-55 |
XCVII | A-56 |
XCIX | A-58 |
C | A-60 |
CI | A-62 |
CII | A-64 |
CIII | A-65 |
CIV | A-67 |
CV | A-69 |
CVI | A-72 |
CVII | A-76 |
CVIII | A-77 |
CIX | A-78 |
CX | A-79 |
CXI | A-81 |
CXII | A-83 |
CXIII | A-85 |
CXIV | A-86 |
CXV | A-88 |
CXVI | A-91 |
CXVII | A-93 |
CXXVII | A-110 |
CXXVIII | A-111 |
CXXIX | A-112 |
CXXX | A-115 |
CXXXI | A-117 |
CXXXII | A-118 |
CXXXIII | A-119 |
CXXXIV | A-121 |
CXXXV | A-122 |
CXXXVI | A-125 |
CXXXVIII | A-127 |
CXXXIX | A-128 |
CXL | A-130 |
CXLI | A-131 |
CXLII | A-132 |
CXLIII | A-133 |
CXLIV | A-136 |
CXLV | A-137 |
CXLVI | A-139 |
CXLVII | A-140 |
CXLVIII | A-141 |
CXLIX | A-142 |
CL | A-143 |
CLI | A-145 |
CLII | A-146 |
CLIII | A-147 |
CLIV | A-150 |
CLVI | A-151 |
CLVIII | A-153 |
CLX | A-154 |
CLXI | A-160 |
CLXII | A-166 |
CLXIII | A-170 |
CLXIV | A-171 |
CLXV | A-175 |
CLXVI | A-177 |
CLXVII | A-180 |
CLXVIII | A-182 |
CLXX | A-1 |
CLXXIII | A-3 |
CLXXV | A-4 |
CLXXVI | A-5 |
CLXXVII | A-7 |
CLXXIX | A-8 |
CLXXX | A-10 |
CLXXXI | A-11 |
CLXXXII | A-12 |
CLXXXIII | A-13 |
CLXXXIV | A-17 |
CLXXXV | A-19 |
CLXXXVI | A-20 |
CLXXXVII | A-21 |
CLXXXVIII | A-23 |
CLXXXIX | A-26 |
CXC | A-28 |
CXCI | A-30 |
CXCII | A-37 |
CXCIII | A-1 |
CXCIV | A-3 |
CXCV | A-5 |
CXCVII | A-6 |
CXCVIII | A-7 |
CXCIX | A-10 |
CC | A-12 |
CCI | A-14 |
CCII | A-15 |
CCIV | A-16 |
CCV | A-18 |
CCVI | A-19 |
CCVII | A-20 |
CCVIII | A-21 |
CCIX | A-22 |
CCX | A-23 |
CCXI | A-25 |
CCXII | A-28 |
CCXIV | A-30 |
CCXV | A-31 |
CCXVI | A-34 |
CCXVII | A-36 |
CCXVIII | A-39 |
CCXIX | A-40 |
CCXX | A-41 |
CCXXI | A-43 |
CCXXII | A-48 |
CCXXIII | A-54 |
CCXXIV | A-59 |
CCXXV | A-62 |
CCXXVI | A-70 |
CCXXVII | A-73 |
A-83 | |
i | |
iii | |