Algebra I Textbook for Students of Mathematics /

• Κύριος συγγραφέας: Gorodentsev, Alexey L. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Θέματα: Mathematics.; Algebra.

This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them...

Πίνακας περιεχομένων:

• Notations and Abbreviations
• 1 Set-Theoretic and Combinatorial Background
• 2 Integers and Residues
• 3 Polynomials and Simple Field Extensions
• 4 Elementary Functions and Power Series Expansions
• 5 Ideals, Quotient Rings, and Factorization
• 6 Vectors
• 7 Duality
• 8 Matrices
• 9 Determinants
• 10 Euclidean Spaces
• 11 Projective Spaces
• 12 Groups
• 13 Description of Groups
• 14 Modules over a Principal Ideal Domain
• 15 Linear Operators
• 16 Bilinear Forms
• 17 Quadratic Forms and Quadrics
• 18 Real Versus Complex
• 19 Hermitian Spaces
• 20 Quaternions and Spinors
• References
• Hints to Selected Exercises
• Index.