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AuthorCohn, Harvey. author
TitleA Classical Invitation to Algebraic Numbers and Class Fields [electronic resource] / by Harvey Cohn
ImprintNew York, NY : Springer New York, 1978
Connect tohttp://dx.doi.org/10.1007/978-1-4612-9950-9
Descript 328p. online resource

CONTENT

I. Preliminaries -- 1. Introductory Remarks on Quadratic Forms -- 2. Algebraic Background -- 3. Quadratic Euclidean Rings -- 4. Congruence Classes -- 5. Polynomial Rings -- 6. Dedekind Domains -- 7. Extensions of Dedekind Domains -- 8. Rational and Elliptic Functions -- II. Ideal Structure in Number Fields -- 9. Basis and Discriminant -- 10. Prime Factorization -- 11. Units -- 12. Geometry of Numbers -- 13. Finite Determination of Class Number -- III. Introduction to Class Field Theory -- 14. Quadratic Forms, Rings and Genera -- 15. Ray Class Structure and Fields, Hilbert Class Fields -- 16. Hilbert Sequences -- 17 Discriminant and Conductor -- 18. The Artin Isomorphism -- 19. The Zeta-Function -- Appendices (by Olga Taussky) -- Lectures on Class Field Theory by E. Artin (Gรถttingen 1932) Notes by O. Taussky -- into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky) -- Subject Matter Index


Mathematics Number theory Mathematics Number Theory



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