Examples of 'homomorphisms' in a sentence
Meaning of "homomorphisms"
In mathematics, a structure-preserving map between two algebraic structures
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- plural of homomorphism
How to use "homomorphisms" in a sentence
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homomorphisms
Functors can be thought of as homomorphisms between categories.
Group homomorphisms are functions that preserve group structure.
The composition of group homomorphisms is again a homomorphism.
The homomorphisms di are called boundary maps.
The composition of two ring homomorphisms is a ring homomorphism.
Monoid homomorphisms are sometimes simply called monoid morphisms.
Clearly composites of homomorphisms are homomorphisms.
It is easy to check that φ and ψ are homomorphisms.
The composition of module homomorphisms is again a module homomorphism.
Similar bialgebras are related by bialgebra homomorphisms.
Almost homomorphisms form an abelian group under pointwise addition.
Any homology theory comes with induced homomorphisms.
Homomorphisms constructed with its help are generally called connecting homomorphisms.
Generalizations such as cobordism also have induced homomorphisms.
Their homomorphisms correspond to invariant differential operators over flag manifolds.
See also
Connectedness is preserved by graph homomorphisms.
Likewise there are induced homomorphisms of higher homotopy groups and homology groups.
Multiplication of real numbers corresponds to functional composition of almost homomorphisms.
For a detailed discussion of relational homomorphisms and isomorphisms see.
The local homomorphisms are all injective for a covering by contractible open sets.
The collection of hypergraphs is a category with hypergraph homomorphisms as morphisms.
The pointwise sum of two rng homomorphisms is generally not a rng homomorphism.
This defines an equivalence relation on the set of almost homomorphisms.
Homomorphisms do not have to map between sets which have the same operations.
Restriction can be generalized to other group homomorphisms and to other rings.
These two homomorphisms are clearly inverse to each other and thus are indeed isomorphisms.
Connection with homomorphisms.
Much of the importance of quotient groups is derived from their relation to homomorphisms.
The class of regular languages is closed under homomorphisms and inverse homomorphisms.
Some scheduling problems can be modeled as a question about finding graph homomorphisms.
The situation for complete lattices with complete homomorphisms obviously is more intricate.
These singleton groups are zero objects in the category of groups and group homomorphisms.
Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon.
In this dissertation we present some results of automatic continuity for banach algebras homomorphisms.
Both are homomorphisms of the kernel of the Hankel transform of a series.
Then one checks that these two functions are in fact both ring homomorphisms.
Consider the category D of homomorphisms of abelian groups.
For distinction we call such algebraic structures rngs and their morphisms rng homomorphisms.
Structures and Homomorphisms.
The theorem also has a natural interpretation in the category of directed graphs and graph homomorphisms.
In general, homomorphisms are neither injective nor surjective.
To add real numbers defined this way we add the almost homomorphisms that represent them.
Under this view, homomorphisms of such structures are exactly graph homomorphisms.
Monomorphisms in Ring are the injective homomorphisms.
Likewise, monoid homomorphisms are just functors between single object categories.
Consider the category Ab of abelian groups and group homomorphisms.
Needless to say, composition of two homomorphisms is also a homomorphism.
The category Mag consisting of all magmas with their homomorphisms.
The homomorphisms and are just the induced homomorphisms from and, respectively.
Consider the category Grp of all groups with group homomorphisms as morphisms.
