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

isomorphic, 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...

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

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

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....

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...

kernel and image of the homomorphism. The homomorphism theorem is used to prove the isomorphism theorems. Given two groups G and H and a group homomorphism...

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

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

However, the isomorphism theorem gives a stronger result, because ring isomorphisms preserve multiplication while module isomorphisms (even between rings)...

Whitney isomorphism theorem states that, for connected graphs with more than four vertices, there is a one-to-one correspondence between isomorphisms of the...

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

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

algebra over a field Noether isomorphism theorems in abstract algebra Max Noether's theorem, several theorems Noether's theorem on rationality for surfaces...

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

Almgren isomorphism theorem is a result in geometric measure theory and algebraic topology about the topology of the space of flat cycles in a Riemannian...

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

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

Dihedral group Dn Quaternion group Q Cauchy's theorem Lagrange's theorem Sylow theorems Hall's theorem p-group Elementary abelian group Frobenius group...

the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of mutual one-one reducibility. Theorem 7.VI, Hartley...

theory, the correspondence theorem (also the lattice theorem, and variously and ambiguously the third and fourth isomorphism theorem) states that if N {\displaystyle...

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

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

homology theory, given a Künneth theorem and a Thom isomorphism for that homology theory. A Thom isomorphism theorem for a homology theory is now viewed...

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

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′...

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