Definition, Betydelse & Synonymer | Engelska ordet ISOMORPHISM

Definition av ISOMORPHISM

1. (matematik) isomorfi

Exempel på hur du använder ISOMORPHISM i en mening

• In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism.
• 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 a homomorphism is given, and of the kernel and image of the homomorphism.
• In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations.
• In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
• In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.
• Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings.
• In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.
• In 1911 Max Dehn proposed that the word problem was an important area of study in its own right, together with the conjugacy problem and the group isomorphism problem.
• Further examples include "up to isomorphism", "up to permutations", and "up to rotations", which are described in the Examples section.
• In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects.
• It states that for the following commutative diagram (in any abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well.
• In the above short exact sequence, where the sequence splits, it allows one to refine the first isomorphism theorem, which states that:.
• Degenerate bilinear form, a bilinear form on a vector space V whose induced map from V to the dual space of V is not an isomorphism.
• Igor Shafarevich conjectured that there are only finitely many isomorphism classes of abelian varieties of fixed dimension and fixed polarization degree over a fixed number field with good reduction outside a fixed finite set of places.
• This stabilizer is (or, more exactly, is isomorphic to) , since the choice of a point as an origin induces an isomorphism between the Euclidean space and its associated Euclidean vector space.
• The amount of freedom in that isomorphism is known as the Galois group of p (if we assume it is separable).
• In the presence of a non-degenerate form (an isomorphism , for instance a Riemannian metric or Minkowski metric), one can raise and lower indices.
• With the delta operator defined by a power series in D as above, the natural bijection between delta operators and polynomial sequences of binomial type, also defined above, is a group isomorphism, in which the group operation on power series is formal composition of formal power series.
• If it does, however, the direct limit is unique in a strong sense: given another direct limit X′ there exists a unique isomorphism X′ → X that commutes with the canonical morphisms.
• In the smooth case, any Riemannian metric or symplectic form gives an isomorphism between the cotangent bundle and the tangent bundle, but they are not in general isomorphic in other categories.

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