The Resource Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics, by Falko Lorenz, (electronic resource)

Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics, by Falko Lorenz, (electronic resource)

Label
Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics
Title
Algebra
Title remainder
Volume II: Fields with Structure, Algebras and Advanced Topics
Statement of responsibility
by Falko Lorenz
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Lorenz, Falko
Dewey number
512
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
gElmtphHXno
Language note
English
LC call number
QA150-272
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Algebra
  • Field theory (Physics)
  • Matrix theory
  • Number theory
  • Algebra
  • Commutative Rings and Algebras
  • Field Theory and Polynomials
  • Linear and Multilinear Algebras, Matrix Theory
  • Number Theory
Label
Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics, by Falko Lorenz, (electronic resource)
Instantiates
Publication
Note
Includes indexes
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (342 p.)
Form of item
online
Isbn
9780387724881
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-387-72488-1
Specific material designation
remote
System control number
  • (CKB)1000000000491934
  • (EBL)3062954
  • (SSID)ssj0000316125
  • (PQKBManifestationID)11207694
  • (PQKBTitleCode)TC0000316125
  • (PQKBWorkID)10264168
  • (PQKB)10078675
  • (DE-He213)978-0-387-72488-1
  • (MiAaPQ)EBC3062954
  • (EXLCZ)991000000000491934
Label
Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics, by Falko Lorenz, (electronic resource)
Publication
Note
Includes indexes
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (342 p.)
Form of item
online
Isbn
9780387724881
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-387-72488-1
Specific material designation
remote
System control number
  • (CKB)1000000000491934
  • (EBL)3062954
  • (SSID)ssj0000316125
  • (PQKBManifestationID)11207694
  • (PQKBTitleCode)TC0000316125
  • (PQKBWorkID)10264168
  • (PQKB)10078675
  • (DE-He213)978-0-387-72488-1
  • (MiAaPQ)EBC3062954
  • (EXLCZ)991000000000491934

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