A First Course in Abstract Algebra: Rings, Groups and Fields, Second Edition Book

1	The natural numbers	3
2	The integers	15
3	Modular arithmetic	31
4	Polynomials with rational coefficients	41
5	Factorization of polynomials	55
6	Rings	73
7	Subrings and unity	89
8	Integral domains and fields	101
9	Polynomials over a field	119
10	Associates and irreducibles	141
11	Factorization and ideals	155
12	Principal ideal domains	169
13	Primes and unique factorization	177
14	Polynomials with integer coefficients	189
15	Euclidean domains	197
16	Ring homomorphisms	211
17	The kernel	225
18	Rings of cosets	237
19	The isomorphism theorem for rings	247
20	Maximal and prime ideals	259
21	The Chinese remainder theorem	271
22	Symmetries of figures in the plane	287
23	Symmetries of figures in space	299
24	Abstract groups	313
25	Subgroups	329
26	Cyclic groups	339
27	Group homomorphisms	357
28	Group isomorphisms	367
29	Permutations and Cayley's theorem	379
30	More about permutations	389
31	Cosets and Lagrange's theorem	399
32	Groups of cosets	413
33	The isomorphism theorem for groups	425
34	The alternating groups	435
35	Fundamental theorem for finite Abelian groups	449
36	Solvable groups	455
37	Constructions with compass and straightedge	465
38	Constructibility and quadratic field extensions	475
39	The impossibility of certain constructions	489
40	Vector spaces I	503
41	Vector spaces II	511
42	Field extensions and Kronecker's theorem	527
43	Algebraic field extensions	537
44	Finite extensions and constructibility revisited	551
45	The splitting field	565
46	Finite fields	577
47	Galois groups	585
48	The fundamental theorem of Galois theory	599
49	Solving polynomials by radicals	615