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Titlebook: Algebra II; Chapters 4 - 7 Nicolas Bourbaki Textbook 2003 Springer-Verlag GmbH Germany, part of Springer Nature 2003 MSC (2000): 12-02, 13-

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期刊全称Algebra II
期刊简称Chapters 4 - 7
影响因子2023Nicolas Bourbaki
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图书封面Titlebook: Algebra II; Chapters 4 - 7 Nicolas Bourbaki Textbook 2003 Springer-Verlag GmbH Germany, part of Springer Nature 2003 MSC (2000): 12-02, 13-
影响因子.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, regularextensions. 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 ve
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发表于 2025-3-21 20:37:43 | 显示全部楼层
Commutative Fields,the algebra homomorphisms are unital, every subalgebra of an algebra contains the unit element of that algebra. Whenever a field K is said to be contained in a ring L (in particular in a field) without further specification, it is understood that K is a subring of L; we shall also say that K is a su
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Ordered groups and fields,ase being that of .. Unless explicitly stated otherwise, we will use . notation for the composition law in all groups and monoids under study. On the other hand, as we go along we will present certain important algebraic applications of the theory of ordered groups and monoids, and we will according
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https://doi.org/10.1007/978-3-658-22046-4the algebra homomorphisms are unital, every subalgebra of an algebra contains the unit element of that algebra. Whenever a field K is said to be contained in a ring L (in particular in a field) without further specification, it is understood that K is a subring of L; we shall also say that K is a su
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https://doi.org/10.1007/978-3-642-61698-3MSC (2000): 12-02, 13-02, 12Fxx, 12J15, 13F10, 13C10, 12E05,; YellowSale2006; commutative fields; order
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978-3-540-00706-7Springer-Verlag GmbH Germany, part of Springer Nature 2003
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Modules over principal ideal domains,Recall (I, p. 104) that an ideal of a commutative ring A is said to be . if it has the form (.)= A. for some . ∈ A.
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