Author | Marcus, Daniel A. author |
---|---|

Title | Number Fields [electronic resource] / by Daniel A. Marcus |

Imprint | New York, NY : Springer New York, 1977 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-9356-6 |

Descript | 292 p. 1 illus. online resource |

SUMMARY

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises

CONTENT

1: A Special Case of Fermatโ{128}{153}s Conjecture -- 2: Number Fields and Number Rings -- 3: Prime Decomposition in Number Rings -- 4: Galois Theory Applied to Prime Decomposition -- 5: The Ideal Class Group and the Unit Group -- 6: The Distribution of Ideals in a Number Ring -- 7: The Dedekind Zeta Function and the Class Number Formula -- 8: The Distribution of Primes and an Introduction to Class Field Theory -- Appendix 1: Commutative Rings and Ideals -- Appendix 2: Galois Theory for Subfields of C -- Appendix 3: Finite Fields and Rings -- Appendix 4: Two Pages of Primes -- Further Reading -- Index of Theorems -- List of Symbols

Mathematics
Algebra
Number theory
Mathematics
Number Theory
Algebra