First Course in Abstract Algebra, A
A broad introduction to abstract algebra that develops concepts in groups, rings, fields, vector spaces, and linear transformations. The book also explores finite structures, symmetry, codes, canonical forms, prime and maximal ideals, Noetherian rings, varieties, Gröbner bases, and the insolvability of the general quintic.
About This Book
This course in abstract algebra introduces foundational ideas through a broad progression of mathematical topics.
Early chapters cover induction, binomial coefficients, greatest common divisors, arithmetic, congruences, set theory, permutations, groups, subgroups, and Lagrange's theorem.
The text develops homomorphisms, quotient groups, group actions, fields, polynomials, quotient rings, finite fields, vector spaces, linear transformations, and determinants.
Later material includes codes, canonical forms, the insolvability of the general quintic, finite abelian groups, the Sylow theorems, prime and maximal ideals, Noetherian rings, varieties, and Gröbner bases.
Additional resources include selected exercise hints, a bibliography, and an index.
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