LDR 02576nac 22003011u 4500 010 _a2225685746 _brel. 090 _a5608 101 _afre 102 _aFR 100 _a20091130 frey50 200 _aEléments de mathématique _bM _ealgèbre _fN. Bourbaki _hChapitres 4 à 7 210 _aParis, _cMasson _d1981 215 _a1 vol. (VII-422 p.) _d24 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 _a12Fxx _bField theory and polynomials _xField extensions _20 686 _9161885 _a13F10 _bCommutative algebra -- Arithmetic rings and other special rings _xPrincipal ideal rings _20 686 _9161854 _a13C10 _bCommutative algebra -- Theory of modules and ideals _xProjective and free modules and ideals _20 686 _9161777 _a12E05 _bField theory and polynomials -- General field theory _xPolynomials (irreducibility, etc.) _20 686 _9161352 _a05E05 _bCombinatorics -- Algebraic combinatorics _xSymmetric functions and generalizations _20 700 _4070 _9173949 _aBourbaki _bNicolas 856 _uhttps://link.springer.com/book/10.1007%2F978-3-540-34499-5 _zed. Springer 905 _agf _b1990 906 _aaw _b2012-08-17 995 _f08043-01 _xachat _98879 _cCMI _20 _kSéries BOU _o0 _eSalle S _bCMI 001 5608