Category
page 1Theorems in ring theory
Hilbert's basis theorem
theorem
Wedderburn's little theorem
theorem that every finite division ring is a field
Artin–Wedderburn theorem
theorem
Gauss's lemma
lemma that the greatest common divisor of the coefficients is a multiplicative function
Nakayama lemma
lemma
freshman's dream
the identity (a+b)ᵖ = aᵖ + bᵖ, which holds if the prime number p>0 is the characteristic of the ring we work in
primary decomposition
in algebra, expression of an ideal as the intersection of ideals of a specific type
Krull's principal ideal theorem
mathematical theorem of dimensional theory
Skolem–Noether theorem
theorem which characterizes the automorphisms of simple rings
Artin–Rees lemma
lemma stating that, given an ideal I in a Noetherian commutative ring R and a submodule N of a a finitely generated R-module M, there exists a positive integer k such that, for every n≥k, IⁿM ∩ N = Iⁿ⁻ᵏ(IᵏM ∩ N)
Going up and going down
concepts in commutative algebra
Hopkins–Levitzki theorem
Jacobson density theorem
mathematical theorem