Algebra Fields and Galois Theory /

• Κύριος συγγραφέας: Lorenz, Falko (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2006.
• Σειρά: Universitext
• Θέματα: Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; Field theory (Physics).; Number theory.; Field Theory and Polynomials.; Commutative Rings and Algebras.; Number Theory.

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 extens...

Πίνακας περιεχομένων:

• 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.