Fraleigh, John B.
A first course in abstract algebra / John B. Fraleigh - 2 ed. - 455 p.
Groups -- Binary operations -- Groups -- Subgroups -- Permutations I y II -- Cyclic groups -- Isomorphism -- Direct products -- Finitely generated abelian gropups -- Groups in geometry and analysis -- Groups of cosets Normal subgroups and factor groups -- Homomorphisms -- series of groups -- The sylow theorems -- Applications of the sylow theory -- Free groups -- Group presentations -- Simplicial complexes and homology groups -- Computations of homology groups -- More homology computations and applications -- Homological algebra -- Rings and fields -- Rings -- Integral domains -- Some noncommutative examples -- The field of quotients of an integral domain -- Our basic goal -- Quotient ring and ideals -- Homomorphisms of rings -- Rings of polynomials -- Factorization of polynomials over a field -- Unique factorization domains -- Euclidean domains -- Gaussian integers and norms -- Introduction to extension fields -- Vector spaces -- Further algebraic structures -- Algebraic extensions -- Geometric constructions -- Automorphisms of fields -- The isomorphism extension theorem -- Splitting fields -- Separable extensions -- Totally inseparable extensions -- Finite fields -- Galois theory -- Illustrations of galois theory -- Cyclotomic extensions -- Insolvability of the quintic --
Algebra
Matematicas
512.02 / F798a
A first course in abstract algebra / John B. Fraleigh - 2 ed. - 455 p.
Groups -- Binary operations -- Groups -- Subgroups -- Permutations I y II -- Cyclic groups -- Isomorphism -- Direct products -- Finitely generated abelian gropups -- Groups in geometry and analysis -- Groups of cosets Normal subgroups and factor groups -- Homomorphisms -- series of groups -- The sylow theorems -- Applications of the sylow theory -- Free groups -- Group presentations -- Simplicial complexes and homology groups -- Computations of homology groups -- More homology computations and applications -- Homological algebra -- Rings and fields -- Rings -- Integral domains -- Some noncommutative examples -- The field of quotients of an integral domain -- Our basic goal -- Quotient ring and ideals -- Homomorphisms of rings -- Rings of polynomials -- Factorization of polynomials over a field -- Unique factorization domains -- Euclidean domains -- Gaussian integers and norms -- Introduction to extension fields -- Vector spaces -- Further algebraic structures -- Algebraic extensions -- Geometric constructions -- Automorphisms of fields -- The isomorphism extension theorem -- Splitting fields -- Separable extensions -- Totally inseparable extensions -- Finite fields -- Galois theory -- Illustrations of galois theory -- Cyclotomic extensions -- Insolvability of the quintic --
Algebra
Matematicas
512.02 / F798a