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| LEADER |
02985nam a2200373 a 4500 |
| 001 |
2005829 |
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20171111235951.0 |
| 008 |
001023s1992 enka ob 001 0 eng d |
| 020 |
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|a 058529447X
|q (electronic bk.)
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| 020 |
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|a 9780585294476
|q (electronic bk.)
|z 0198534558
|q (hardback)
|q (pbk.)
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| 040 |
|
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|a N$T
|b eng
|e pn
|z 019853454X
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| 050 |
|
4 |
|a QA247
|b .E39 1992eb
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| 100 |
1 |
4 |
|a Ellis, Graham.
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| 245 |
1 |
0 |
|a Rings and fields /
|c Graham Ellis.
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| 260 |
1 |
0 |
|a Oxford [England] :
|b Clarendon Press ;
|c 1992.
|a New York :
|b Oxford University Press,
|
| 300 |
1 |
0 |
|a 1 online resource (viii, 169 pages) :
|b illustrations.
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| 490 |
1 |
0 |
|a Oxford science publications
|
| 504 |
1 |
0 |
|a Includes bibliographical references (page 166) and index.
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| 505 |
0 |
0 |
|a 0. Preliminaries. Definition of rings and fields. Vector spaces. Bases. Equivalence relations. Axiom of choice -- 1. Diophantine equations: Euclidean domains. Euclidean domain of Gaussian integers. Euclidean domains as unique factorization domains -- 2. Construction of projective planes: splitting fields and finite fields. Existence and uniqueness of splitting fields and of finite fields of prime power order -- 3. Error codes: primitive elements and subfields. Existence of primitive elements in finite fields. Subfields of finite fields. Computation of minimum polynomials -- 4. Construction of primitive polynomials: cyclotomic polynomials and factorization. Basic properties of cyclotomic polynomials. Berlekamp's factorization algorithm -- 5. Ruler and compass constructions: irreducibility and constructibility. Product formula for the degree of composite extensions. Irreducibility criteria for polynomials over the rationals. The field of constructible real numbers -- 6. Pappus' theorem and Desargues' theorem in projective planes: Wedderburn's theorem. Proof of Wedderburn's theorem -- 7. Solution of polynomials by radicals: Galois groups. Basic definitions and results in Galois groups. Discriminants -- 8. Introduction to groups. Group axioms. Subgroup lattice. Class equation. Cauchy's theorem. Transitive permutation groups. Soluble groups -- 9. Cryptography: elliptic curves and factorization. Euler's function. Discrete logarithms. Elliptic curves. Pollard's method of factorizing integers. Elliptic curve factorization of integers.
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| 650 |
0 |
0 |
|a Rings (Algebra)
|
| 650 |
0 |
0 |
|a Algebraic fields.
|
| 650 |
0 |
6 |
|a Anneaux (Algèbre)
|
| 650 |
0 |
6 |
|a Corps algébriques.
|
| 650 |
0 |
7 |
|a MATHEMATICS
|x Algebra
|x Intermediate.
|
| 650 |
0 |
7 |
|a Algebraic fields.
|
| 650 |
0 |
7 |
|a Rings (Algebra)
|
| 650 |
1 |
7 |
|a Ringen (wiskunde)
|
| 650 |
1 |
7 |
|a Veldentheorie.
|
| 650 |
1 |
7 |
|a Corps algébriques.
|
| 650 |
1 |
7 |
|a Anneaux (Algèbre)
|
| 952 |
|
|
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