User:Linus44

Rings
PIDs, UFDs, Noetherian rings

Polys
Polynomial_Factor_Theorem

Polynomial_Forms_over_a_Field_is_Principal_Ideal_Domain

Epimorphism_from_Polynomial_Forms_to_Polynomial_Functions

Definition:Integral_Polynomial

Definition:Irreducible_Polynomial

Definition:Root_of_a_Polynomial

Division_Theorem_for_Polynomial_Forms_over_a_Field

Set of Polynomials is a Subring

Ring of Polynomial Forms is Integral Domain

Rings of Polynomial Forms Isomorphic

Definition_of_Polynomial_from_Polynomial_Ring

1-var polynomial rings, Fields, extensions, algebraic extensions, algebraic clusure, separable extensions, splitting fields, normal extensions, galois extensions, polynomials, cyclotomy, norm and trace.

Commutative algebra
Definitions

Definition:Jacobson Radical Definition:Nilpotent Element Definition:Nilradical

Definition:Radical Ideal

Definition:Radical of an Ideal

Definition:Reduced Ring

Little theorems

Characterisation of the Jacobson Radical

Cayley-Hamilton Theorem

Hilbert's Basis Theorem

Nakayama's Lemma

Radical Ideal iff Quotient Ring is Reduced

Analytic Number Theory
Definition:Dirichlet_Series

Dirichlet_Series_Absolute_Convergence_Lemma

Abscissa_of_Absolute_Convergence

Dirichlet_Series_Convergence_Lemma

Abscissa_of_Convergence

Difference_of_Abscissae_of_Convergence