Algebra

Algebra
-0 %
Volume I: Fields and Galois Theory
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Artikel-Nr:
9780387289304
Veröffentl:
2005
Erscheinungsdatum:
08.12.2005
Seiten:
296
Autor:
Falko Lorenz
Gewicht:
426 g
Format:
234x165x15 mm
Sprache:
Englisch
Beschreibung:

From Math Reviews:
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 book ends with an appendix containing exercises and notes on the
previous parts of the book. However, brief historical comments and
suggestions for further reading are also scattered through the text.

From Math Reviews: "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. Thus, for instance, the transformation of the classical geometrical problems on constructions with ruler and compass in their algebraic setting in the first chapter introduces the reader spontaneously to such fundamental algebraic notions as field extension, the degree of an extension, etc... The book ends with an appendix containing exercises and notes on the previous parts of the book. However, brief historical comments and suggestions for further reading are also scattered through the text."

From Math Reviews:This is a charming textbook, introducing the reader to the classicalparts of algebra. The exposition is admirably clear and lucidlywritten with only minimal prerequisites from linear algebra...The book ends with an appendix containing exercises and notes on theprevious parts of the book. However, brief historical comments andsuggestions for further reading are also scattered through the text.
Constructibility with Ruler and Compass.- Algebraic Extensions.- Simple Extensions.- Fundamentals of Divisibility.- Prime Factorization in Polynomial Rings. Gauss's Theorem.- Polynomial Splitting Fields.- Separable Extensions.- Galois Extensions.- Finite Fields, Cyclic Groups and Roots of Unity.- Group Actions.- Applications of Galois Theory to Cyclotomic Fields.- Further Steps into Galois Theory.- Norm and Trace.- Binomial Equations.- Solvability of Equations.- Integral Ring Extensions with Applications to Galois Theory.- The Transcendence of ?.- Fundamentals of Transcendental Field Extensions.- Hilbert's Nullstellensatz.

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