<p>The English translation of the new and expanded version of Bourbaki's "Algèbre", Chapters 4 to 7 completes Algebra, 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 has been 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.</p>

Algebra II: Chapters 4-7 (Elements of Mathematics)

Science & Math

Paul M. Cohn

Nicolas Bourbaki

J. Howie

Mathematics

Springer Nature

The main emphasis of this revised algebra textbook is on fields, rings and modules. The text includes new chapters on the representative theory of finite groups, coding theory and algebraic language theory. Sets, lattices, categories and graphs are introduced at the beginning of the text. The text, which has been rewritten with the aim of making the subject easier to grasp, contains simplified proofs and many new illustrations and exercises.

Algebra

John Wiley & Sons, Ltd.

This is the third and final volume of a popular algebra textbook, which is being published in paperback at a reduced rate.

Algebra (v. 3)

John Wiley and Sons Ltd.

<p>Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.</p>

Further Algebra and Applications

Springer

This Book is Brand new international softcover edition delivered within 7-12 working days via UPS/USPS/DHL and FEDEX.(FOR SALE ONLY U.S. & U.K.)

Basic Algebra: Groups, Rings, and Fields

SPRINGER (SIE)