The interpretation must be a homomorphism, while valuation is simply a function.
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Thus an embedding is the same thing as a strong homomorphism which is one-to-one.
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Isomorphisms, automorphisms, and endomorphisms are all types of homomorphism.
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A homomorphism between two associative R-algebras is an R-linear ring homomorphism.
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A field automorphism is a bijectivering homomorphism from a field to itself.
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Note that this homomorphism maps the natural numbers back into themselves.
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In the language of abstract algebra, a linear map is a homomorphism of vector spaces.
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This is because a bijective homomorphism need not be an isomorphism of topological groups.
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This gives a homomorphism from de Rham cohomology to singular cohomology.
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More examples
Similarity of form
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the Greek language: (homos) meaning "same" and (morphe) meaning "shape".
The term *-algebra is defined below after first defining a *-ring.
In the mathematical field of graph theory a graph homomorphism is a mapping between two graphs that respects their structure. More concretely it maps adjacent vertices to adjacent vertices.
(homomorphic) Similar looking forms.
(homomorphic) usually referring to achenes in a capitulum which are all similar.
A mapping between mathematical structures of the same type (e. g. groups or rings) that preserves the structure, i. e. f(ab) = f(a)f(b).