close
1.

図書

図書
Lindsay N. Childs
出版情報: Providence, R.I. : American Mathematical Society, c2000  viii, 215 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 80
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Hopf algebras and Galois extensions
Hopf Galois structures on separable field extensions
Tame extensions and Noether's theorem
Hopf algebras of rank $p$ Larson orders
Cyclic extensions of degree $p$
Non-maximal orders Ramification restrictions
Hopf algebras of rank $p^2$
Cyclic Hopf Galois extensions of degree $p^2$
Formal groups
Principal homogeneous spaces and formal groups
Bibliography
Index
Introduction
Hopf algebras and Galois extensions
Hopf Galois structures on separable field extensions
2.

図書

図書
Lindsay Childs
出版情報: New York : Springer, c1979  xiv, 338 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Numbers / Chapter 1:
Induction / Chapter 2:
Another Form of Induction / A.:
Well-Ordering / C.:
Division Theorem / D.:
Bases / E.:
Operations in Base a / F.:
Euclid's Algorithm / Chapter 3:
Greatest Common Divisors
Bezout's Identity
The Efficiency of Euclid's Algorithm
Euclid's Algorithm and Incommensurability
Unique Factorization / Chapter 4:
The Fundamental Theorem of Arithmetic
Exponential Notation
Primes
Primes in an Interval
Congruences / Chapter 5:
Congruence Modulo m
Basic Properties
Divisibility Tricks
More Properties of Congruence
Linear Congruences and Bezout's Identity
Congruence Classes / Chapter 6:
Congruence Classes (mod m): Examples
Congruence Classes and Z/mZ
Arithmetic Modulo m
Complete Sets of Representatives
Units
Applications of Congruences / Chapter 7:
Round Robin Tournaments
Pseudorandom Numbers
Factoring Large Numbers by Trial Division
Sieves
Factoring by the Pollard Rho Method
Knapsack Cryptosystems
Rings and Fields / Chapter 8:
Axioms
Z/mZ
Homomorphisms
Fermat's and Euler's Theorems / Chapter 9:
Orders of Elements
Fermat's Theorem
Euler's Theorem
Finding High Powers Modulo m
Groups of Units and Euler's Theorem
The Exponent of an Abelian Group
Applications of Fermat's and Euler's Theorems / Chapter 10:
Fractions in Base a
RSA Codes
2-Pseudoprimes
Trial a-Pseudoprime Testing
The Pollard p - 1 Algorithm
On Groups / Chapter 11:
Subgroups
Lagrange's Theorem
A Probabilistic Primality Test
Some Nonabelian Groups
The Chinese Remainder Theorem / Chapter 12:
The Theorem
Products of Rings and Euler's [phi]-Function
Square Roots of 1 Modulo m
Matrices and Codes / Chapter 13:
Matrix Multiplication
Linear Equations
Determinants and Inverses
M[subscript n](R)
Error-Correcting Codes, I
Hill Codes
Polynomials / Chapter 14:
Primitive Roots / Chapter 15:
Factorization into Irreducible Polynomials
The Fundamental Theorem of Algebra / Chapter 16:
Rational Functions
Partial Fractions
Irreducible Polynomials over R
The Complex Numbers
Root Formulas
The Fundamental Theorem
Integrating / G.:
Derivatives / Chapter 17:
The Derivative of a Polynomial
Sturm's Algorithm
Factoring in Q[x], I / Chapter 18:
Gauss's Lemma
Finding Roots
Testing for Irreducibility
The Binomial Theorem in Characteristic p / Chapter 19:
The Binomial Theorem
Fermat's Theorem Revisited
Multiple Roots
Congruences and the Chinese Remainder Theorem / Chapter 20:
Congruences Modulo a Polynomial
Applications of the Chinese Remainder Theorem / Chapter 21:
The Method of Lagrange Interpolation
Fast Polynomial Multiplication
Factoring in F[subscript p][x] and in Z[x] / Chapter 22:
Berlekamp's Algorithm
Factoring in Z[x] by Factoring mod M
Bounding the Coefficients of Factors of a Polynomial
Factoring Modulo High Powers of Primes
Primitive Roots Modulo m / Chapter 23:
Polynomials Which Factor Modulo Every Prime
Cyclic Groups and Primitive Roots / Chapter 24:
Cyclic Groups
Primitive Roots Modulo p[superscript e]
Pseudoprimes / Chapter 25:
Lots of Carmichael Numbers
Strong a-Pseudoprimes
Rabin's Theorem
Roots of Unity in Z/mZ / Chapter 26:
For Which a Is m an a-Pseudoprime?
Square Roots of -1 in Z/pZ
Roots of -1 in Z/mZ
False Witnesses
Proof of Rabin's Theorem
RSA Codes and Carmichael Numbers
Quadratic Residues / Chapter 27:
Reduction to the Odd Prime Case
The Legendre Symbol
Proof of Quadratic Reciprocity
Applications of Quadratic Reciprocity
Congruence Classes Modulo a Polynomial / Chapter 28:
The Ring F[x]/m(x)
Representing Congruence Classes mod m(x)
Inventing Roots of Polynomials
Finding Polynomials with Given Roots
Some Applications of Finite Fields / Chapter 29:
Latin Squares
Error Correcting Codes
Reed-Solomon Codes
Classifying Finite Fields / Chapter 30:
More Homomorphisms
On Berlekamp's Algorithm
Finite Fields Are Simple
Factoring x[superscript pn] - x in F[subscript p][x]
Counting Irreducible Polynomials
Finite Fields
Most Polynomials in Z[x] Are Irreducible
Hints to Selected Exercises
References
Index
Introduction
Numbers / Chapter 1:
Induction / Chapter 2:
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼