{"product_id":"9783540007067","title":"Algebra II: Chapters 4 - 7","description":"\u003ch1\u003eAlgebra II: Chapters 4 - 7\u003c\/h1\u003e \u003ch2\u003eBourbaki, N.; Cohn, P.M.; Howie, J.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, \u003cem\u003eAlgèbre\u003c\/em\u003e, Chapters 4 to 7 (1981). \u003c\/p\u003e\n\u003cp\u003eThis completes \u003cem\u003eAlgebra\u003c\/em\u003e, 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.\u003c\/p\u003e\n\u003cp\u003eChapter IV: Polynomials and Rational Fractions\u003c\/p\u003e\n\u003cp\u003eChapter V: Commutative Fields\u003c\/p\u003e\n\u003cp\u003eChapter VI: Ordered Groups and Fields\u003c\/p\u003e\n\u003cp\u003eChapter VII: Modules Over Principal Ideal Domains\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2003-04-16\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540007067\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-61698-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 453\u003c\/p\u003e ","brand":"Masson","offers":[{"title":"Default Title","offer_id":44341332639884,"sku":"9783540007067","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540007067.jpg?v=1775773004","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783540007067","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}