Definition & Betydelse | Engelska ordet HOMOMORPHISMS

Definition av HOMOMORPHISMS

1. böjningsform av homomorphism

Exempel på hur man kan använda HOMOMORPHISMS i en mening

• With a direct product, we get some natural group homomorphisms for free: the projection maps defined by.
• 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.
• It follows that the rings forms a category with ring homomorphisms as morphisms (see Category of rings).
• Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of the category of sets and/or restrict the arrows to functions of a particular kind.
• Functors and natural transformations abound in algebraic topology, with the Hurewicz homomorphisms serving as examples.
• 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.
• Note that commutativity is crucial here; it ensures that the sum of two group homomorphisms is again a homomorphism.
• In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
• In the language of category theory, a homology theory is a type of functor from the category of the mathematical object being studied to the category of abelian groups and group homomorphisms, or more generally to the category corresponding to the associated chain complexes.
• ) Because of the faithfulness of the functor U, the homomorphisms of a concrete category may be formally identified with their underlying functions (i.
• The way they are put together is specified by a system of homomorphisms (group homomorphism, ring homomorphism, or in general morphisms in the category) between those smaller objects.
• In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions.
• This is contained in the Jacobson radical, which is the intersection of all maximal ideals, which are the kernels of homomorphisms to fields.
• Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms.
• The category of rings (whose morphisms are unit-preserving ring homomorphisms) forms a non-full subcategory of the category of rngs.
• This means that P is projective if and only if this functor preserves epimorphisms (surjective homomorphisms), or if it preserves finite colimits.
• By the Gelfand–Naimark theorem, the category of localizable measurable spaces (with measurable maps) is equivalent to the category of commutative Von Neumann algebras (with normal unital homomorphisms of *-algebras).
• Probably the most general duality that is classically referred to as "Stone duality" is the duality between the category Sob of sober spaces with continuous functions and the category SFrm of spatial frames with appropriate frame homomorphisms.
• The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the surjective group homomorphisms, and the isomorphisms are the bijective group homomorphisms.
• Since injective left modules extend homomorphisms from all left ideals to R, injective modules are clearly divisible in sense 2 and 3.

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