{"product_id":"algebra-ii-chapters-4-7-9783540007067","title":"Algebra II: Chapters 4 - 7","description":"\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-643713\"\u003eN. Bourbaki\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 04\/16\/2003\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 453\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.52lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.24h x 6.35w x 1.00d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9783540007067\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 3540007067\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-COM\"\u003eComputers\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-COM014000\"\u003eComputer Science\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT034000\"\u003eMathematical Analysis\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT005000\"\u003eCalculus\u003c\/a\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eThis title is not returnable\u003c\/i\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":44590011973869,"sku":"9783540007067","price":119.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_8089c9dd-1c9d-4bd9-b677-75e41d3fdc57.jpg?v=1702252500","url":"https:\/\/sureshotbooks.com\/es\/products\/algebra-ii-chapters-4-7-9783540007067","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}