A Survey of Modern AlgebraMacmillan, 1977 - 500 pagine A new edition of the classic undergraduate text introducing abstract algebra using concrete examples. The authors ground their explanations with computational and theoretical exercises to develop the student's "power to think for himself," covering topics such as the role of careful proof in algebra, linear algebra as grounded in geometry, groups as expressions of symmetry, and subgroups and subsystems leading to lattice theory. This volume is a corrected version of the 4th edition and is offered by a new publisher. Annotation copyrighted by Book News, Inc., Portland, OR |
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a₁ affine affine transformation algebraic numbers automorphism b₁ basis bijection canonical form cardinal number coefficients column commutative ring complex numbers conjugate contains coordinates Corollary correspondence cosets cyclic group defined definition degree determined diagonal direct sum distributive law divisor elements entries equivalent Euclidean Exercises factors field F finite formula function Galois group given group G hence homomorphism ideal identity implies integral domain inverse irreducible irreducible polynomial isomorphic lattice Lemma linear combination linear transformation linearly independent matrix minimal polynomial monic multiplication nonsingular nonzero normal subgroup one-one ordered field orthogonal permutation plane positive integers postulates Proof properties proves Theorem quadratic form rational numbers real numbers root field root of unity row space row-equivalent S₁ satisfies scalar Show solution spanned square subfield subset subspace symmetric Theorem 13 unique upper bound vector space y₁ zero