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 A₂ abelian group algebraically closed AutKF b₁ basis char commutative ring Consequently contains Corollary cyclic D₁ defined Definition denoted direct sum disjoint division ring divisors element endomorphism epimorphism equivalent EXAMPLE Exercise extension field ɛ G F₁ factors finite dimensional free module function functor G₁ Galois group given group G H₁ hence Hint implies integral domain intermediate field invertible irreducible isomorphism K-algebra K₁ Ker f left Artinian left ideal left R-module Lemma Let F Let G linear linearly independent matrix monic monomorphism morphism multiplicative n₁ nilpotent Noetherian nonempty nonzero normal subgroup P₁ phism polynomial prime ideal principal ideal domain Proposition quotient R-module R-module homomorphism r₁ resp ring with identity root Section semisimple SKETCH OF PROOF solvable splitting field subfield subgroup of G submodule subset Theorem 1.6 u₁ unique vector space Verify whence x₁ zero