Index of names

B, C, D, E, F, G, H, I, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y Z.

A

Action of a group

Algebraic element

algebraically closed field

Automorphism

B

Binary Operation

Burnside's Theorem

C

Canonical projection

Cardano, Cardano's formula see cubic equations

Cartesian Product

Cardinality of sets

Cauchy and Sylow theorems

Cayley

Characteristic

commutative ring

complement of a set

Complex Conjugate

complex numbers

Completing the square

Composition

congruence classes modulo n: ℤ/nℤ

conjugates elements over fields

Correspondence Theorem for Rings

Cubic equations

Cyclotomic polynomials

D

D_n, Dihedral groups

Degree

De Moivre’s theorem

De Morgan's laws

Denumerable set

Difference of powers formula

Direct

Distributive law

division ring (aka skew-field)

Divisibility Criteria

Doubling the cube

E

Eisenstein’s irreducibility criterion

Elementary Symmetric fuctions (polynomials)

equipollent sets (see cardinality)

Eratosthenes' sieve

Equivalence

Eratosthenes' sieve

Euclidean

Euclid’s Theorem on Primes

Euler

Function and theorem

Extension

F

Factor ring (see quotient rings)

Fermat, Pierre de

Ferrari, Ludovico, see quartic equations

Ferro, Scipione del, see cubic equations.

Field

Fior, Antonio Maria, see cubic equations.

Frobenius' automorphism

G

Galois

Gaussian integers

GCD

Group

H

Homomorphisms

I

Identity function

Indicator function (see characteristic function)

Isomorphism

of rings

Integral domain

Inseparable polynomials

Induction

Injective function

Inverse function

Invertible

Polynomials
Elements of ℤ_n U(ℤ_n): Euler function, Modular arithmetic

Irreducibile

K

L

Lagrange's Thereom

Least common multiple

Linear congruences

M

Minimal Polynomial

Modulo relation: ≡

Modulo p Irreducibility Test for rational polynomials

Modulus of a complex number

Monic polynomial

Monomorphism

multiplication

N

Norm

of a complex number

Normal subgroups

Normal extensions

O

onto function (Surjective)

order

P

Partial Fraction Decomposition

Pigeon-hole principle

Polynomials

Prime

Primitive

Primitive Element Theorem

Principal ideal domain

Q

ℚ, rational numbers

Quadratic equation

Quartic equations

Quotient rings

modulo an ideal I; R/I
modulo the ideal ⟨p(x)⟩: K[x]/(p(x))

Quotient fields

R

Rational Functions

Rational numbers, ℚ

Rational root theorem

Rectification of the circle

RSA encryption (Rivest, Shamir, and Adleman)

Ruffini's theorem

root

of unity

S

Symmetric group

Separable

Sieve of Eratosthenes

Simple Extensions

skew-field (division ring)

Splitting Field

Squaring the circle

Strong induction

Surjective function (onto)

Sylow

Symmetric fuctions (polynomials)

T

trascendental element

Totient function (Euler's φ function)

Triangle inequality

U

Unique Factorization in Polynomial Domains

U(ℤ_n), Euler function

V

Vieta's formulas

W

Wedderburn's theorem

Wilson's Theorem

Well-Ordering principle

Z

The ℤ/nℤ group