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- 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,

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