A first course in abstract algebra /

Detalles Bibliográficos
Autor principal: Fraleigh, John B.
Otros Autores: Katz, Victor J.
Formato: Libro
Lenguaje:English
Publicado: Boston : Addison-Wesley, 2003.
Edición:Seventh edition.
Materias:
Álgebra abstracta
Tabla de Contenidos:
  • Sets and relations
  • I. Groups and subgroups. Introduction and examples ; Binary operations ; Isomorphic binary structures ; Groups ; Subgroups ; Cyclic groups ; Generating sets and Cayley Digraphs
  • II. Permutations, cosets, and direct products. Groups of permutations ; Orbits, cycles, and the alternating groups ; Cosets and the theorem of Lagrange ; Direct products and finitely generated Abelian groups ; Plane isometries
  • III. Homomorphisms and factor groups. Homomorphisms ; Factor groups ; Factor-group computations and simple groups ; Group action on a set ; Applications of G-sets to counting
  • IV. Rings and fields. Rings and fields ; Integral domains ; Fermat's and Euler's theorems ; The field of quotients of an integral domain ; Rings of polynomials ; Factorization of polynomials over a field ; Noncommutative examples ; Ordered rings and fields
  • V. Ideals and factor rings. Homomorphisms and factor rings ; Prime and maximal ideas ; Gröbner bases for ideals
  • VI. Extension fields. Introduction to extension fields ; Vector spaces ; Algebraic extensions ; Geometric constructions ; Finite fields
  • VII. Advanced group theory. Isomorphism theorems ; Series of groups ; Sylow theorems ; Applications of the Sylow theory ; Free Abelian groups ; Free groups ; Group presentations
  • VIII. Groups in topology. Simplicial complexes and homology groups ; Computations of homology groups ; More homology computations and applications ; Homological algebra
  • IX. Factorization. Unique factorization domains ; Euclidean domains ; Gaussian integers and multiplicative norms
  • X. Automorphisms and Galois theory. Automorphisms of fields ; The isomorphism extension theorem ; Splitting fields ; Separable extensions ; Totally inseparable extensions ; Galois theory ; Illustrations of Galois theory ; Cyclotomic extensions ; Insolvability of the quintic
  • Appendix: Matrix algebra.

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