Classic AlgebraFundamental to all areas of mathematics, algebra provides the cornerstone for the student?s development. The concepts are often intuitive, but some can take years of study to absorb fully. For over twenty years, the author?s classic three-volume set, Algebra, has been regarded by many as the most outstanding introductory work available. This work, Classic Algebra, combines a fully updated Volume 1 with the essential topics from Volumes 2 and 3, and provides a self-contained introduction to the subject. In addition to the basic concepts, advanced material is introduced, giving the reader an insight into more advanced algebraic topics. The clear presentation style gives this book the edge over others on the subject. Undergraduates studying first courses in algebra will benefit from the clear exposition and perfect balance of theory, examples and exercises. The book provides a good basis for those studying more advanced algebra courses.
|
Contents
Integers and rational numbers | 21 |
Groups | 40 |
Vector spaces and linear mappings | 66 |
Copyright | |
10 other sections not shown
Other editions - View all
Common terms and phrases
a₁ abelian group algebra automorphism B₁ basis bijection bilinear called characteristic coefficients columns commutative coprime corresponding cosets cyclic group Deduce defined degree denote determinant diagonal direct sum eigenvalues endomorphism equation Euclidean expressed factors field F field of fractions finite group finite-dimensional follows function given group G hence hermitian homomorphism ideal induction injective inner product integral domain inverse irreducible isomorphism lemma Let F Let G linear mapping linearly independent module monoid morphism multiplication normal obtain orthogonal orthonormal p₁ permutation polynomial positive integer prime number principal ideal domain proof prove rational numbers ring satisfies Show solution spanning square matrix submodule subring subset subspace Sylow p-subgroup symmetric THEOREM u₁ unique unitary unitary space V₁ vector space Verify write written x₁ zero