A first course in abstract algebra / (Record no. 14466)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02839cam a2200205 a 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0201763907 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780201763904 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0321156080 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780321156082 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.92 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Fraleigh, John B |
| 245 12 - TITLE STATEMENT | |
| Title | A first course in abstract algebra / |
| 250 ## - EDITION STATEMENT | |
| Edition statement | Seventh edition |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xii, 520 pages : |
| Other physical details | illustrations ; |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 -- Gr©œbner 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 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebra, Abstract |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Katz, Victor J |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Books |
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