Author | Lang, Serge. author |
---|---|
Title | Undergraduate Algebra [electronic resource] / by Serge Lang |
Imprint | New York, NY : Springer New York, 1987 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9234-7 |
Descript | IX, 379 p. 1 illus. in color. online resource |
I The Integers -- ยง1. Terminology of Sets -- ยง2. Basic Properties -- ยง3. Greatest Common Divisor -- ยง4. Unique Factorization -- ยง5. Equivalence Relations and Congruences -- II Groups -- ยง1. Groups and Examples -- ยง2. Mappings -- ยง3. Homomorphisms -- ยง4. Cosets and Normal Subgroups -- ยง5. Permutation Groups -- ยง6. Cyclic Groups -- ยง7. Finite Abelian Groups, -- III Rings -- ยง1. Rings -- ยง2. Ideals -- ยง3. Homomorphisms -- ยง4. Quotient Fields -- IV Polynomials -- ยง1. Euclidean Algorithm -- ยง2. Greatest Common Divisor -- ยง3. Unique Factorization -- ยง4. Partial Fractions -- ยง5. Polynomials over the Integers -- ยง6. Transcendental Elements -- ยง7. Principal Rings and Factorial Rings -- V Vector Spaces and Modules -- ยง1. Vector Spaces and Bases -- ยง2. Dimension of a Vector Space -- ยง3. Matrices and Linear Maps -- ยง4. Modules -- ยง5. Factor Modules -- ยง6. Free Abelian Group -- VI Some Linear Groups -- ยง1. The General Linear Group -- ยง2. Structure of GL2(F) -- ยง3. SL2(F) -- VII Field Theory -- ยง1. Algebraic Extensions -- ยง2. Embeddingsโ -- ยง3. Splitting Fieldsโ -- ยง4. Galois Theory -- ยง5. Quadratic and Cubic Extensions -- ยง6. Solvability by Radicals -- ยง7. Infinite Extensions -- VIII Finite Fields -- ยง1. General Structure -- ยง2. The Frobenius Automorphism -- ยง3. The Primitive Elements -- ยง4. Splitting Field and Algebraic Closure -- ยง5. Irreducibility of the Cyclotomic Equation over Q -- ยง6. Where Does It All Go? Or Rather, Where Does Some of It Go? -- IX The Real and Complex Numbers -- ยง1. Ordering of Rings -- ยง2. Preliminaries -- ยง3. Construction of the Real Numbers -- ยง4. Decimal Expansions -- ยง5. The Complex Numbers -- X Sets -- ยง1. More Terminology -- ยง2. Zonaโs Lemma -- ยง3. Cardinal Numbers -- ยง4. Well-ordering -- ยง1. The Natural Numbers -- ยง2. The Integers -- ยง3. Infinite Sets