specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among...
25 KB (3,466 words) - 23:17, 17 September 2024
isomorphic, with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique. The term isomorphism is mainly used for algebraic...
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Thom space (redirect from Thom isomorphism theorem)
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...
13 KB (1,978 words) - 18:32, 31 July 2024
in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs...
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two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural isomorphism. Let H {\displaystyle H} be a Hilbert space over a...
75 KB (12,630 words) - 11:15, 13 July 2024
Topological group (redirect from Birkhoff–Kakutani theorem)
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...
50 KB (7,492 words) - 02:08, 28 September 2024
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....
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order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...
25 KB (3,028 words) - 20:53, 28 July 2024
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...
8 KB (1,307 words) - 20:37, 15 March 2024
of a ring Isomorphism theorems theorems that assert that some homomorphisms involving quotients and subobjects are isomorphisms Isomorphism (sociology)...
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In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...
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Modular lattice (redirect from Diamond isomorphism theorem)
ψ indicated by the arrows are mutually inverse isomorphisms. Failure of the diamond isomorphism theorem in a non-modular lattice. The composition ψφ is...
19 KB (2,397 words) - 12:00, 4 June 2024
Kernel (algebra) (category Isomorphism theorems)
However, the isomorphism theorem gives a stronger result, because ring isomorphisms preserve multiplication while module isomorphisms (even between rings)...
18 KB (2,553 words) - 15:03, 27 August 2024
of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets...
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Line graph (redirect from Whitney graph isomorphism theorem)
Whitney isomorphism theorem states that, for connected graphs with more than four vertices, there is a one-to-one correspondence between isomorphisms of the...
43 KB (5,299 words) - 10:28, 5 July 2024
algebra over a field Noether isomorphism theorems in abstract algebra Max Noether's theorem, several theorems Noether's theorem on rationality for surfaces...
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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...
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Universal algebra (section Some basic theorems)
coordinatewise. The isomorphism theorems, which encompass the isomorphism theorems of groups, rings, modules, etc. Birkhoff's HSP Theorem, which states that...
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theory, the correspondence theorem (also the lattice theorem, and variously and ambiguously the third and fourth isomorphism theorem) states that if N {\displaystyle...
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an injective reduction, and a computable isomorphism is a bijective reduction. Myhill's isomorphism theorem: Two sets A , B ⊆ N {\displaystyle A,B\subseteq...
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Bernoulli scheme (redirect from Ornstein's theorem)
operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is...
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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...
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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...
73 KB (6,015 words) - 12:17, 2 August 2024
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...
92 KB (12,132 words) - 22:29, 5 July 2024
In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov...
5 KB (675 words) - 10:58, 18 August 2023
Homomorphism (section Isomorphism)
isomorphic to X / ∼ {\displaystyle X/\!\sim } ; this fact is one of the isomorphism theorems. When the algebraic structure is a group for some operation, the...
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Image (mathematics) (category Isomorphism theorems)
Dihedral group Dn Quaternion group Q Cauchy's theorem Lagrange's theorem Sylow theorems Hall's theorem p-group Elementary abelian group Frobenius group...
19 KB (2,429 words) - 17:46, 27 July 2024
lattice theorem. Several important properties of quotient groups are recorded in the fundamental theorem on homomorphisms and the isomorphism theorems. If...
20 KB (3,749 words) - 01:49, 28 September 2024
the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of mutual one-one reducibility. Theorem 7.VI, Hartley...
1 KB (180 words) - 20:09, 27 March 2024
Zassenhaus lemma (category Isomorphism theorems)
{\displaystyle D\triangleleft C} are normal subgroups. Then there is an isomorphism of quotient groups: ( A ∩ C ) B ( A ∩ D ) B ≅ ( A ∩ C ) D ( B ∩ C ) D...
3 KB (404 words) - 20:46, 19 November 2021