{"product_id":"algebra-ii-chapters-4-7-paperback","title":"Algebra II: Chapters 4 - 7 - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eN. Bourbaki\u003c\/b\u003e (Author), \u003cb\u003eP. M. Cohn\u003c\/b\u003e (Translator), \u003cb\u003eJ. Howie\u003c\/b\u003e (Translator)\u003c\/p\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 \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, regular extensions. 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 \u003cp\u003eChapter IV: Polynomials and Rational Fractions\u003c\/p\u003e \u003cp\u003eChapter V: Commutative Fields\u003c\/p\u003e \u003cp\u003eChapter VI: Ordered Groups and Fields\u003c\/p\u003e \u003cp\u003eChapter VII: Modules Over Principal Ideal Domains\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 453\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.24 x 6.35 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e April 16, 2003\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47212919914745,"sku":"9783540007067","price":129.58,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/N3F4RWhuUXZIU3FYRC9UajdveTRwZz09.webp?v=1768098993","url":"https:\/\/bookscloud.io\/products\/algebra-ii-chapters-4-7-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}