Abstract

1: Rings. 2: Euclidean rings. 3: Highest common factor. 4: The four-squares theorem. 5: Fields and polynomials. 6: Unique factorization domains. 7: Field of quotients of an integral domain. 8: Factorization of polynomials. 9: Fields and field extensions. 10: Finite cyclic groups and finite fields. 11: Algebraic numbers. 12: Ruler and Compass constructions. 13: Homomorphisms, ideals and factor rings. 14: Principal ideal domains and a method for constructing fields. 15: Finite fields. Solutions to selected exercises. References

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