{"product_id":"algebra-ii-chapters-4-7-9783540007067","title":"Algebra II: Chapters 4 - 7","description":"\u003cp\u003e • Author(s): N. Bourbaki\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Computer Science\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, 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 \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","brand":"Springer","offers":[{"title":"Paperback","offer_id":45284041228439,"sku":"9783540007067","price":4366.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783540007067.webp?v=1769280001","url":"https:\/\/atlanticbooks.com\/products\/algebra-ii-chapters-4-7-9783540007067","provider":"Atlantic Books","version":"1.0","type":"link"}