Cantitate/Preț
Produs

Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics: Universitext

Autor Falko Lorenz Traducere de Silvio Levy
en Limba Engleză Paperback – 27 dec 2007
From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume II the reader can find: the theory of ordered fields (e.g., with reformulation of the fundamental theorem of algebra in terms of ordered fields, with Sylvester's theorem on the number of real roots), Nullstellen-theorems (e.g., with Artin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentals of the theory of quadratic forms, of valuations, local fields and modules. The book also contains some lesser known or nontraditional results; for instance, Tsen's results on solubility of systems of polynomial equations with a sufficiently large number of indeterminates. These two volumes constitute a very good, readable and comprehensive survey of classical algebra and present a valuable contribution to the literature on this subject.
Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (2) 44577 lei  6-8 săpt.
  Springer – 8 dec 2005 44577 lei  6-8 săpt.
  Springer – 27 dec 2007 44820 lei  6-8 săpt.

Din seria Universitext

Preț: 44820 lei

Nou

Puncte Express: 672

Preț estimativ în valută:
8578 8917$ 7106£

Carte tipărită la comandă

Livrare economică 04-18 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9780387724874
ISBN-10: 0387724877
Pagini: 336
Ilustrații: X, 340 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.49 kg
Ediția:2008
Editura: Springer
Colecția Springer
Seria Universitext

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

Ordered Fields and Real Fields.- Hilbert's Seventeenth Problem and the Real Nullstellensatz.- Orders and Quadratic Forms.- Absolute Values on Fields.- Residue Class Degree and Ramification Index.- Local Fields.- Witt Vectors.- The Tsen Rank of a Field.- Fundamentals of Modules.- Wedderburn Theory.- Crossed Products.- The Brauer Group of a Local Field.- Local Class Field Theory.- Semisimple Representations of Finite Groups.- The Schur Group of a Field.

Recenzii

From the reviews:
“The approach taken by the author is very straightforward, both in its presentation of proofs and its examples. Unlike some books, it is very possible to teach yourself the subject using this book. … Out of all the books I used in undergrad, this one was one of my favorites because it was easy to use for reference and for independent learning. … Great foundation establishing book to start building in the domain of Abstract Algebra.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)
"Algebra II: Fields with Structure, Algebras and Advanced Topics is … a complete algebra course, including both undergraduate and graduate topics. … The second volume focuses on fields with structure and algebras. … the choice of topics and their organization are excellent and provide a unifying view of most of algebra. In all, Lorenz’s book is a wonderful reference for both teachers and researches, and can be used with much profit for independent study by hard-working students." (Luiz Hendrique de Figueiredo, MathDL, July, 2008)
"The author has managed to cover such an amazing wealth of advanced material in a very adroit manner, thereby keeping the representation utmost lively, comprehensible, thorough, always straight to the point, essentially self-contained, methodologically elegant and – all in all – admirably reader-friendly. … No doubt, this is an outstanding textbook on advanced topics in abstract algebra, mainly in its field-theoretic and number-theoretic aspects, and its availability in English makes it a unique and utmost valuable enrichment of the international textbook literature on the subject." (Werner Kleinert, Zentralblatt MATH, Vol. 1130 (8), 2008)

Textul de pe ultima copertă

The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra.
The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry.
The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.
Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students.
 
From Reviews of the German version:
This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the
framework of the development of carefully selected problems.
- Stefan Porubsky, Mathematical Reviews

Caracteristici

Nicely written comprehensive survey of classical algebra Includes unique collection of topics Author provides enough detail that the only prerequisite is basic knowledge of algebra