{"product_id":"algebra-ii-chapters-4-7-von-n-bourbaki","title":"Algebra II","description":"\n                                \n                \u003cp\u003e\n                                        This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, \n                    \n                    \u003cem\u003eAlgèbre\u003c\/em\u003e\n                                        , Chapters 4 to 7 (1981). \n                \n                \u003c\/p\u003e\n                                \n                \n                \u003cp\u003e\n                                        This completes \n                    \n                    \u003cem\u003eAlgebra\u003c\/em\u003e\n                                        , 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 vector spaces. Sections on semi-simple endomorphisms and Jordan decomposition have been added.\n                \n                \u003c\/p\u003e\n                                \n                \n                \u003cp\u003eChapter IV: Polynomials and Rational Fractions\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eChapter V: Commutative Fields\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eChapter VI: Ordered Groups and Fields\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eChapter VII: Modules Over Principal Ideal Domains\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540007067\"\u003e\u003ch3\u003eChapters 4 - 7\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783540007067","offer_id":39426407628893,"sku":"9783540007067","price":64.19,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4878e698-f47e-4a1e-8ba8-2a6cec860836.jpg?v=1772172097","url":"https:\/\/shop.autorenwelt.de\/en\/products\/algebra-ii-chapters-4-7-von-n-bourbaki","provider":"Autorenwelt Shop","version":"1.0","type":"link"}