Fundamental 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.
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Integers and rational numbers
Vector spaces and linear mappings
8 other sections not shown
abelian group algebra automorphism basis bijection bilinear called characteristic coefficients columns composition series conjugacy class conjugate contains coprime corresponding cosets cyclic group Deduce defined degree denote determinant diagonal direct product direct sum eigenvalues endomorphism equation Euclidean example expressed factors field finite group finite-dimensional follows function G-module given group G hence hermitian holds homomorphism induction infinite injective integral domain inverse irreducible isomorphism lemma Let G linear mapping linearly independent maximal minimal module monoid morphism multiplication n x n nilpotent non-singular normal subgroup obtain orthogonal permutation polynomial positive integer prime number principal ideal domain Proof prove rank representation result satisfies semisimple Show similarly solution spanned square matrix subgroup of G submodule subring subset subspace surjective Sylow subgroup symmetric THEOREM unique unitary vector space Verify write written zero