This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is 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 are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What's more, the book contains some lesser known or nontraditional results - for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.
Publisher: Springer-Verlag New York Inc.
Number of pages: 340
Weight: 532 g
Dimensions: 235 x 155 x 18 mm
Edition: 2008 ed.
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)