algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates the structure...

algebraic structure, the fundamental theorem on homomorphisms (or first isomorphism theorem) states that image of a homomorphism is isomorphic to the quotient...

isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects...

Fundamental theorem of Galois theory Fundamental theorem of geometric calculus Fundamental theorem on homomorphisms Fundamental theorem of ideal theory...

prototypical example of an abelian category. Homomorphism Fundamental theorem on homomorphisms Quasimorphism Ring homomorphism Dummit, D. S.; Foote, R. (2004). Abstract...

will be used as the base of all fundamental groups. The inclusion maps of U1 and U2 into X induce group homomorphisms j 1 : π 1 ( U 1 , x 0 ) → π 1 (...

Fundamental theorem on homomorphisms (abstract algebra) Isomorphism theorem (abstract algebra) Lattice theorem (abstract algebra) 15 and 290 theorems...

The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector...

i m ( f ) {\displaystyle \mathrm {im} (f)} ⁠. (See also: Fundamental theorem on homomorphisms.) The ideals of R {\displaystyle R} and R   /   I {\displaystyle...

Brouwer fixed point theorem and the Borsuk–Ulam theorem in dimension 2. The fundamental group of the figure eight is the free group on two letters. The idea...

representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper...

Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The...

Factor group Fundamental theorem on homomorphisms Group homomorphism Group isomorphism Homomorphism Isomorphism theorem Inner automorphism Order automorphism...

and its homomorphisms as a category, a subvariety U of V is a full subcategory of V, meaning that for any objects a, b in U, the homomorphisms from a to...

their relation to homomorphisms. The first isomorphism theorem states that the image of any group G {\displaystyle G} under a homomorphism is always isomorphic...

properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a homomorphism from G ∗ H to K. Unless one of the...

In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix...

of the situation, which thus get lost on the way. In certain situations (such as descent theorems for fundamental groups à la Van Kampen) it is much more...

homotopy induce homomorphisms that are inverse to each other. A common use of induced homomorphisms is the following: by showing that a homomorphism with certain...

differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. In particular, the fundamental theorem of calculus...

The relationship between ideals, homomorphisms, and factor rings is summed up in the fundamental theorem on homomorphisms. radical The radical of an ideal...

Lie's third theorem: Every finite-dimensional real Lie algebra is the Lie algebra of some simply connected Lie group. The homomorphisms theorem: If ϕ : Lie...

of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep results...

mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then...

the fundamental theorem of finitely generated abelian groups. The existence of algorithms for Smith normal form shows that the fundamental theorem of finitely...

details follow. Group theorist László Fuchs states: As far as the fundamental theorem on finite abelian groups is concerned, it is not clear how far back...

HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for...

mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result...

is noetherian, this follows from the fundamental theorem below (in particular, Krull's principal ideal theorem), but it is also a consequence of a more...

of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications...