Category: Theorems in abstract algebra

Latimer–MacDuffee theorem
The Latimer–MacDuffee theorem is a theorem in abstract algebra, a branch of mathematics. It is named after Claiborne Latimer and Cyrus Colton MacDuffee, who published it in 1933. Significant contribut
Fundamental lemma (Langlands program)
In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was co
Gabriel–Popescu theorem
In mathematics, the Gabriel–Popescu theorem is an embedding theorem for certain abelian categories, introduced by Pierre Gabriel and Nicolae Popescu. It characterizes certain abelian categories (the G
Fundamental theorem on homomorphisms
In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates the structure of two objects between which
Abhyankar's conjecture
In abstract algebra, Abhyankar's conjecture is a 1957 conjecture of Shreeram Abhyankar, on the Galois groups of algebraic function fields of characteristic p. The soluble case was solved by Serre in 1
Strassmann's theorem
In mathematics, Strassmann's theorem is a result in field theory. It states that, for suitable fields, suitable formal power series with coefficients in the valuation ring of the field have only finit
Abhyankar's lemma
In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if
Quillen–Suslin theorem
The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between free modules and projective modules over polyno
Abhyankar's inequality
Abhyankar's inequality is an inequality involving extensions of valued fields in algebra, introduced by Abhyankar. If K/k is an extension of valued fields, then Abhyankar's inequality states that the
Dold–Kan correspondence
In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence (named after Albrecht Dold and Daniel Kan) states that there is an equivalence between the category of (no
Primitive element theorem
In field theory, the primitive element theorem is a result characterizing the finite degree field extensions that can be generated by a single element. Such a generating element is called a primitive
Dimension theorem for vector spaces
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is
Joubert's theorem
In polynomial algebra and field theory, Joubert's theorem states that if and are fields, is a separable field extension of of degree 6, and the characteristic of is not equal to 2, then is generated o
Eckmann–Hilton argument
In mathematics, the Eckmann–Hilton argument (or Eckmann–Hilton principle or Eckmann–Hilton theorem) is an argument about two unital magma structures on a set where one is a homomorphism for the other.
Structure theorem for finitely generated modules over a principal ideal domain
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generate
Andreotti–Grauert theorem
In mathematics, the Andreotti–Grauert theorem, introduced by Andreotti and Grauert, gives conditions for cohomology groups of coherent sheaves over complex manifolds to vanish or to be finite-dimensio
Cartan's theorem
No description available.
Isomorphism extension theorem
In field theory, a branch of mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field.
Generic flatness
In algebraic geometry and commutative algebra, the theorems of generic flatness and generic freeness state that under certain hypotheses, a sheaf of modules on a scheme is flat or free. They are due t
Segal's conjecture
Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the sta
Whitehead's lemma
Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form is equivalent to the identity matrix by elementary transformations (that is,