Algebra I Textbook for Students of Mathematics /
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...
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| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edition: | 1st ed. 2016. |
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| Online Access: | https://doi.org/10.1007/978-3-319-45285-2 |
Table of Contents:
- 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.