Algebraic theory of quadratic numbers [Documento electrónico] / Mak Trifković
Language: eng.Country: US - United States of America.Publication: New York, NY : Springer , 2013Description: XI, 197 p. : il.ISBN: 978-1-4614-7717-4.Series: UniversitextSubject - Topical Name: Teoria dos números algébricos Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA247.SPR FCT 81496 (Browse shelf(Opens below)) | 1 | Available |
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QA247.SPR FCT 80938 Extensions of rings and modules | QA247.SPR FCT 81083 Graded syzygies | QA247.SPR FCT 81155 Lattice-ordered rings and modules | QA247.SPR FCT 81496 Algebraic theory of quadratic numbers | QA247.SPR FCT 81534 Mean field games and mean field type control theory | QA247.SPR FCT 81669 Ring and module theory | QA247.SPR FCT 81830 Dimension theory of hyperbolic flows |
Colocação: Online
By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.
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