ADVANCED ALGEBRA
A
B C D E F G H I K L M N O P Q R S T U V
W
A
Abbreviation
Abelian group
Abelian group
Abstract real field
Addition
Addition and multiplication of matrices
of degree n
Affine geometry
Affine space
Algebraic over K
Algorithm of division
Algorithm of division
Algorithm of h.c.f
Alteration of first kind
Alteration of second kind
Alterations of first and second kind
Alternating polynomials
Analysis
Application to the theory of linear
substitutions of a complex variable
Applications to the theory of numbers
Approximate computation of roots by
Horner's scheme
Approximating entities
Approximation by rational functions
Associated
elements
Associates
Associative Law
Associative law
Associative law for matrices
Associative law of addition
Automorphism
Automorphism
Automorphism of a normal extension
B
Base
Base
of vectors
Bilinear form
Binomial
equations
Bi-quadratic equations
Budan-Fourier Theorem
C
Calculus of Differences
Canonical
form of matrix
Case r' = 1
Case r' = r
Changes of sign
Characteristic equation
Characteristic polynomial
Characteristic polynomial
Characteristic polynomial with n
different roots
Characteristic polynomials with any
number of roots
Characteristic polynomials with n
different roots
Characteristic polynomials with single
root: General case
Circles enclosing roots of f (x)
Class of residues modulo g
Classes form a ring R(D)
Classes of matrices
Classes of residues
Closed
fields
Coefficients
Coefficients of the highest term equal 1
Co-factor
Column addition
Column vector
Column vector
Commutative group
Commutative Law
Commutative law
Commutative law and matrices
Commutative ring
Commutative rings of polynomials
Commutative sub-ring
Comparison between R and R[x]
Comparison of different methods for
solving systems of linear equations
Complete continued fraction
Complex numbers
Complex roots
Composition of transformations
Conclusion
by induction
Congruence by matrix multiplication
Congruence not special case of
similarity
Congruent
Congruent
matrices
Congruent matrices
Conjugate
elements
Continued fraction
Continued Fraction, convergent of
Continued fraction, convergents of
Continued fraction, distribution along
real axis
Continued fraction, finite
Continued fraction, infinite
Continued fraction, last element of
Continued fraction, purely periodic
Continued fractionm complete
Continued fractions with elements f(x)
Continued fractions with polynomial
elements
Continued fractions with rational
elements
Continued fractions, finite
Continued fractions, simple
Convergence of continued fractions
Convergents
Convergents of a continued fraction
Coordinates
Correspondence between positive numbers
and rational positive expansions
Criterion for uniqueness of
factorization
Cubic equations
Cyclic order
Cyclotomic polynomials of order n
D
Decomposition of matrices
Definition of polynomial
Degree
Degree of freedom
Degree
of matrix
Degree of polynomial
Derivative
Derivatives
Determinant divisors
Determinant of matrix product
Determinant,
properties
Diagonal matrix
Dialogue1
Discriminant
Distribution of continued fraction along
real axis
Distributive laws
Distributive
laws of addition
Divergent
series
Divisible
Domain of integral numbers
Domains with factorizable elements
Duality
E
Eisenstein's Theorem
Element of a field F"
Elementary
arithmetic
Elementary divisors
Elementary matrix
Elementary symmetric polynomials
Elementary Theory of Numbers
Elements
Elements of continued fraction
Elliptic
transformation
Equal
Equivalence
Equivalence
Equivalence, improper
Equivalence, proper
Equivalent
Equivalent
element
Error
Euclidean domains
Euler 's formula
Even numbers
Even permutations
Existence of a root in a suitable
extension
Expansion of f(x) as a
polynomial in x - q
Expansion of quadratic elements into
periodic continued fractions
Expansion of square roots
Expansion of the elements of B
into continued fractions
Exponent
of vector
Extend
Extension by roots of irreducible
polynomials
Extension of a field
Extension of a field to a ring and field
in a finite number of steps
Extension of results of Chapter 1 to
vector space over arbitrary field
Extension of ring
Extension of the isomorphism I
Extensions of F containing a
root of f(x)
F
Factorizable
Factorization
Factorization in D[x]
Factorization in F[x]
Factorization of f(x)
into linear factors
Factors
Field
Field B
Field
of rational numbers
Field of real numbers
Fields
Fields of Characteristic 0
Fields of Characteristics p
Finite continued fraction
Finite continued fractions
Finite extensions
First Distributive Law
Fixed point
Functional
notation
Fundamental laws of algebra
Fundamental Theorem of Classical Algebra
Fundamental Theorem of General Algebra
Fundamentals of General Algebra
G
Gauss' Theorem
General case of resultant
General properties of continued
fractions
Generalizations of the theorem on normal
extensions
Generalized cofactors
General method for irreducibility
Geometry
Graeffe's Method
Group G(K,n)
H
Height
of vector
Highest common factor
Highest common factor and extension of a
field
Homogeneous linear equations
Homogeneous of degree m
Homogeneous polynomials
Homomorphic
Homomorphism
Homomorphism modulo a prime element
Horner's modified scheme
Horner's scheme
Hyperbolic
transformation
I
Identification
Identify
Image of original element
Independence of n-vectors
Independence of vectors
Indeterminate
Infinite
continued fraction
Infinite point of complex sphere
Infinity
Integral domain
Integral domain
Integral Domain
Integral domains
Integral function over C
Integral functions
Integral rational function over C
Integral symmetric functions
Interpolation
Interpolation by iteration
Invariant
Inverse matrix
Inverse of a linear transformation
Irrational positive numbers
Irreducibility in R[x]
Irreducibility of determinants
Irreducible polynomials
Isomorphism
Italic characters
K
Kakeya's Theorem
L
Lagrange's formula
Lagrange's method
Lagrange's
symbols
Last element of continued fraction
Law of reflexivity
Law of symmetry
Law of transitivity
Legendre polynomials
Length
of n-vector
Lill's
rectangular method
Linear equations
Linear interpolation
Linear representation of a resultant
Linear transformation of a vector space
W over K
Link between roots of a polynomial and
those of its derivative
Loxodromic
class
M
Magnitude of a root
Main Theorem for symmetric polynomials
Main theorem on similarity of matrices
Map
Mathematical Induction
Matrices
Matrices and forms
Matrix
columns
Matrix notation and formulae
Matrix over field K
Matrix
row
Matrix row
operations
Matrix,
Rank of
Measurement
of degree of approximation of power series
Meet
Meet of modules
Mesh of a base
Method for calculation of roots
Method of homomorphism
Method of orthogonalization
Metric space
Minors of a determinant
Module
Module
Module over F
Monotony of C(b)
Multiple roots
Multiple roots of a characteristic
polynomial
Multiplication
Multiplicative commutative group
N
Negative
Nest of intervals
Newton's formula
Newton's method
no solution
Non-homogeneous linear equations
Non-separable
Non-Separable Polynomials
Norm
Normal extension
Normal extension of a field
Normal extension of field
Notation
of vectors
Null element
Number
Numbers
n-vectors
O
Odd numbers
Odd
permutations
Operations in a module
order
of integer
Orthogonal system
Orthogonality
P
Parabolic
Transfomation
Partition into classes
Pell's Equation
Periodic sequence
Permutation, composition of
Permutation, cyclic
Permutation, identical
Permutations
Permutations as linear transformations
Permutations, Decomposition of
Permutations, even and odd
Plane geometry
Points
Polynomials
Polynomials in two indeterminates
Polynomials in x over R
Polynomials of which A is a root
Polynomials of which A is a root
Poulain's Theorem
Power
Power
sums
Powers
of matrices
Presentation of permutations
Prime element of an extension
Prime-element
Prime-field
Prime-fields
Primitive element of an extension
Primitive polynomial
Primitive roots
Primitive roots
Principle of mathematical induction
Product
Product of matrices
Product
of matrices
Projective Geometry
Proper and improper equivalence
Properties of
determinants
Pure mathematics
Purely periodic continued fraction
Purely periodic continued fractions
Q
Quadratic form
Quotient fields
Radical
R
Radicals
Rank
Rank of a field over a field
Rational numbers
Rational operations
Rational positive numbers
Real and complex roots
Real distinct roots
Real numbers
Reciprocity
Reduced
quadratic number
Reduced quadratic numbers
Reduced
root
Reducible
Reduction of investigation of
irreducibility in D[x]
Relation between a field and its
subrings.
Remainder
Repeated extension of a field
Representation of positive numbers by
continued fractions
Representative of a class
Resultant
Resultants
Ring of classes of residues generated by
a homomorphism
Ring over V
Ring R(D)
Ring R(J, n)
Ring R(K[x], n)
Rings
Rings of polynomials
Roman characters
Root
Root of a polynomial
Roots in any particular field
Roots of complex polynomials
Roots of real polynomials
Rotations
Row
vector
S
Scalar product
Scalar product
Scalars
Scheme for computations
Second Distributive Law
Seed
of theory
Separable
Separation
of roots
Similar
matrix
Similarity
of space
Simple continued fractions
Simple roots
Singular element
Singular elements
Smallest extension of K admitting
complete reduction of f(x)
Solution
of homogeneous equations
Solution of special equations by
radicals
Solution of systems of linear equations
by means of determinants
Solving an algebraic equation
Space notation
Special matrices
Sturm
chain
Sturm's theorem
Sub-field
Sub-fields of a field
Sub-group
Sub-module
Sub-ring
Sub-rings of a field
Sub-space
Subtraction
Subtraction
Sufficient
sum
Sweep out
"Sweep
out" for matrices of R(D,n)
Symbolic sum
Symmetric polynomials
Symmetric rational functions
T
Test of irrationality
Theorem on integral numbers
Theory of algebraic functions
Transcendental over K
Transform
of matrix
Transformation of vector spaces
Transformations with characteristic
polynomial (l - x)r
Transposed matrix
Transposition
U
Unique
factorization
Unique factorization
Uniquely factorizable
Unit element
unit matrix
Unities
Unit-vector
V
Variable
Vector
independence
Vector space
Vector space over F of Rank n
Vector
spaces
Vector spaces over a field
Vectors
Vectors
W
Weight
of term