An edition of A First Course in Abstract Algebra [Seventh 7th Edition]
(1969)
A first course in abstract algebra
7th ed. (Indian Subcontinent version)
by John B. Fraleigh
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Previews available in: English
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![Cover of: A First Course in Abstract Algebra [RENTAL EDITION]](http://covers.openlibrary.org/b/id/14124282-S.jpg "Cover of: A First Course in Abstract Algebra [RENTAL EDITION]")
A First Course in Abstract Algebra [RENTAL EDITION]
Feb 21, 2020, Pearson
paperback
0136731627 9780136731627
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A first course in abstract algebra
2014, Dorling Kindersley (India) Pvt. Ltd., Pearson India Education Services Pvt. Ltd.
in English
- 7th ed. (Indian Subcontinent version)
933251903X 9789332519039
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First Course in Abstract Algebra: Pearson New International Edition
2013, Pearson Higher Education & Professional Group
in English
1292024968 9781292024967
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![Cover of: A First Course in Abstract Algebra [Seventh 7th Edition]](http://covers.openlibrary.org/b/id/8620256-S.jpg "Cover of: A First Course in Abstract Algebra [Seventh 7th Edition]")
A First Course in Abstract Algebra [Seventh 7th Edition]
Jun 28, 2003, Pearson
8177589008 9788177589009
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First Course in Abstract Algebra
2002, Pearson Education, Limited
in English
0321156080 9780321156082
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Book Details
Table of Contents
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.
Edition Notes
Includes index.
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