specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among...

with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique. The term isomorphism is mainly used for algebraic...

B} be a real vector bundle of rank n. Then there is an isomorphism called a Thom isomorphism Φ : H k ( B ; Z 2 ) → H ~ k + n ( T ( E ) ; Z 2 ) , {\displaystyle...

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...

image of the homomorphism. The homomorphism theorem is used to prove the isomorphism theorems. Similar theorems are valid for vector spaces, modules, and...

ψ indicated by the arrows are mutually inverse isomorphisms. Failure of the diamond isomorphism theorem in a non-modular lattice. The composition ψφ is...

in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs...

order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...

in V such that Tx = 0. The kernel is a subspace of V. The first isomorphism theorem for vector spaces says that the quotient space V/ker(T) is isomorphic...

In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov...

and only if it is continuous at some point. An isomorphism of topological groups is a group isomorphism that is also a homeomorphism of the underlying...

an isomorphism of A {\displaystyle {\mathcal {A}}} with a substructure of B {\displaystyle {\mathcal {B}}} . If it can be written as an isomorphism with...

three isomorphism theorems, called homomorphism theorem, and two laws of isomorphism when applied to groups, appear explicitly. Lasker–Noether theorem In...

of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets...

between isomorphisms of the graphs and isomorphisms of their line graphs. Analogues of the Whitney isomorphism theorem have been proven for the line graphs...

operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is...

an injective reduction, and a computable isomorphism is a bijective reduction. Myhill's isomorphism theorem: Two sets A , B ⊆ N {\displaystyle A,B\subseteq...

two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural isomorphism. Let H {\displaystyle H} be a Hilbert space over a...

T)=\dim(\operatorname {Domain} (T)).} This theorem can be refined via the splitting lemma to be a statement about an isomorphism of spaces, not just dimensions....

of a ring Isomorphism theorems theorems that assert that some homomorphisms involving quotients and subobjects are isomorphisms Isomorphism (sociology)...

{\displaystyle \ker \phi } is trivial. The result follows by use of the first isomorphism theorem, from which we get I m ϕ ≅ G {\displaystyle \mathrm {Im} \,\phi \cong...

mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field. The theorem states that...

coimage is canonically isomorphic to the image by the first isomorphism theorem, when that theorem applies. More generally, in category theory, the coimage...

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

coordinatewise. The isomorphism theorems, which encompass the isomorphism theorems of groups, rings, modules, etc. Birkhoff's HSP Theorem, which states that...

theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which...

a unique isomorphism, or more precisely: if q : Y → Q and q′ : Y → Q′ are two cokernels of f : X → Y, then there exists a unique isomorphism u : Q → Q′...

"The Consistency Strengths of Some Finite Forms of the Higman and Kruskal Theorems". In Friedman, Harvey; Harrington, L. A. (eds.). Harvey Friedman's research...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

is considered to be part of the theorem. A theory is called categorical if it has only one model, up to isomorphism. This term was introduced by Veblen...