LDR 02576nac  22003011u 4500
010    _a2225685746
090    _a5608
101    _afre
102    _aFR
100    _a20091130              frey50       
200    _aEléments de mathématique
       _fN. Bourbaki
       _hChapitres 4 à 7
210    _aParis,
215    _a1 vol. (VII-422 p.)
300    _aExercices en fin de chapitres
320    _aBibliogr. p. [405-406]. Index
330    _aChapter 4 develops the abstract theory of general polynomial rings, function fields, and formal power series, including the differential aspects (differentials and derivations) of these topics as a fundamental part. This is enriched by an in-depth treatment of symmetric tensor algebras, divided powers, polynomial maps, and their functorial interrelations, on the one hand, and by a just as comprehensive discussion of symmetric polynomials, symmetric rational functions, symmetric power series, resultants, and discriminants, on the other. Chapter 5 is then devoted to the theory of commuative fields, their various kinds of extensions, and the allied theory of étale algebras over a ground field. Apart from the fundamentals of Galois theory, Kummer theory, Artin-Schreier theory, and of the theory of finite fields, this chapter also discusses separable algebras and differential criteria for separability in full generality and detail. Chapter 6 briefly describes the basics of ordered groups and ordered fields, together with their respective fundamental structure theorems, whereas Chapter 7 deals with the theory of modules over a principal domain and its applications to the study of endomorphisms of finite-dimensional vector spaces. (Zentralblatt)
676    _a2010
686    _9161785
       _bField theory and polynomials
       _xField extensions
686    _9161885
       _bCommutative algebra -- Arithmetic rings and other special rings
       _xPrincipal ideal rings
686    _9161854
       _bCommutative algebra -- Theory of modules and ideals
       _xProjective and free modules and ideals
686    _9161777
       _bField theory and polynomials -- General field theory
       _xPolynomials (irreducibility, etc.)
686    _9161352
       _bCombinatorics -- Algebraic combinatorics
       _xSymmetric functions and generalizations
700    _4070
856    _uhttps://link.springer.com/book/10.1007%2F978-3-540-34499-5
       _zed. Springer
905    _agf
906    _aaw
995    _f08043-01
       _kSéries BOU
       _eSalle S
001     5608
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