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20220616085931.0 |
| 008 |
130807s2003 maua b 001 0 eng d |
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|a (Sirsi) i9780201763904
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|d UV#
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|a QA162
|b F72 F5 2003
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|a 512/.02
|
| 100 |
1 |
|
|a Fraleigh, John B.
|9 399413
|
| 245 |
1 |
2 |
|a A first course in abstract algebra /
|c John B. Fraleigh ; historical notes by Victor Katz.
|
| 250 |
|
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|a Seventh edition.
|
| 260 |
|
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|a Boston :
|b Addison-Wesley,
|c 2003.
|
| 300 |
|
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|a xii, 520 páginas :
|b ilustraciones ;
|c 24 cm.
|
| 504 |
|
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|a Incluye bibliografía (páginas 483-485) e índice.
|
| 505 |
0 |
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|a 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.
|
| 650 |
|
7 |
|a Álgebra abstracta
|9 2554
|
| 700 |
1 |
|
|a Katz, Victor J.
|9 380977
|
| 776 |
0 |
8 |
|i Online version:
|a Fraleigh, John B.
|t First course in abstract algebra.
|b 7th ed.
|d Boston : Addison-Wesley, 2003
|w (OCoLC)655687263
|
| 901 |
|
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|a Z0
|b UV#
|
| 902 |
|
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|a DGBUV
|
| 596 |
|
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|a 10
|
| 942 |
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|c LIBRO
|
| 999 |
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|c 267502
|d 267502
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