AlgebraAlgebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth. |
Contents
Prerequisites and Preliminaries | 1 |
Functions | 3 |
Relations and Partitions | 6 |
Copyright | |
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a₁ abelian group algebraically closed b₁ basis chain condition char commutative ring Consequently contains Corollary cyclic defined Definition denoted direct sum disjoint division ring divisors element endomorphism epimorphism equivalent EXAMPLE Exercise exists extension field ɛ G factors finite dimensional free module function functor G₁ Galois group given group G hence Hint implies infinite integral domain intermediate field invertible irreducible isomorphism K-algebra left Artinian left ideal left R-module Lemma Let F Let G linear linearly independent matrix monic monomorphism morphism multiplicative nilpotent Noetherian nonempty nonzero normal subgroup P₁ phism polynomial positive integer prime ideal primitive principal ideal domain Proposition quotient R-module R-module homomorphism r₁ radical resp ring with identity root Section semisimple SKETCH OF PROOF solvable splitting field subfield subgroup of G submodule subset Sylow Theorem 1.6 u₁ unique vector space Verify whence zero