Basic Algebra I: Second EditionA classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references. Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as Lie and Jordan algebras, lattices, and Boolean algebras. Exercises appear throughout the text, along with insightful, carefully explained proofs. Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication. |
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a e F abelian group associative assume automorphism base bijective bilinear form called clear coefficients commutative complex numbers composition composition algebra condition consider contains cosets cyclic group define definition denote determined distinct division ring divisor domain endomorphism equations exercise exists extension field factors field F finite finite dimensional finite group finite number finite set first fixed formula function Galois group group G Hence homomorphism ideal implies indeterminates induction infinite invertible irreducible isomorphism lattice LEMMA Let F Let G linear transformation matrix minimum polynomial module monic monoid monomorphism multiplication non-degenerate normal subgroup obtain orthogonal pair partially ordered set permutation positive integer prime Proof prove quadratic form real numbers result roots satisfies sequence Show solvable splitting field subfield subgroup of G submodule submonoid subring subset subspace suppose symmetric symplectic theorem theory vector space