A first course in abstract algebra / John B. Fraleigh ; historical notes by Victor Katz.
Tipo de material:![Texto](/opac-tmpl/lib/famfamfam/BK.png)
- 0201763907
- 9780201763904
- 512.02 23
Tipo de ítem | Biblioteca actual | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems | |
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Biblioteca Yachay Tech | 512.02 F812f 2003 (Navegar estantería(Abre debajo)) | Ej. 1 | Prestado | 04/30/2024 | 005746 |
Includes index.
Includes bibliographical references (pages 483-485).
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.
Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.
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