How do you use Homomorphism in a sentence? See 10+ example sentences showing how this word appears in different contexts, including synonyms like similarity, plus the exact meaning.
Homomorphism meaning
- A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.
- A similar appearance of two unrelated organisms or structures, as for example with fish and whales.
Synonyms of Homomorphism
Using Homomorphism
- The main meaning on this page is: A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces. | A similar appearance of two unrelated organisms or structures, as for example with fish and whales.
- Useful related words include: homomorphy, similarity.
- In the example corpus, homomorphism often appears in combinations such as: ring homomorphism, homomorphism is, group homomorphism.
Context around Homomorphism
- Average sentence length in these examples: 22.9 words
- Position in the sentence: 8 start, 11 middle, 1 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Homomorphism
- In this selection, "homomorphism" usually appears in the middle of the sentence. The average example has 22.9 words, and this corpus slice is mostly made up of statements.
- Around the word, ring, group, semigroup, induces and monomorphismmain stand out and add context to how "homomorphism" is used.
- Recognizable usage signals include a bijective homomorphism between them and a group homomorphism. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "homomorphism" sits close to words such as abatement, abductions and abdulrahman, which helps place it inside the broader word index.
Example types with homomorphism
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Any bijective ring homomorphism is a ring isomorphism. (8 words)
Conversely, the kernel of any semigroup homomorphism is a semigroup congruence. (11 words)
Equivalently, it is a diffeomorphism which is also a group homomorphism. (11 words)
Any such homomorphism is called a (permutation) representation of G on M. For any permutation group, the action that sends (g, x) → g(x) is called the natural action of G on M. This is the action that is assumed unless otherwise indicated. (43 words)
Not every semigroup homomorphism is a monoid homomorphism, since it may not map the identity to the identity of the target monoid, even though the element it maps the identity to will be an identity of the image of the mapping. (41 words)
A group homomorphism between two groups "preserves the group structure" in a precise sense – it is a "process" taking one group to another, in a way that carries along information about the structure of the first group into the second group. (41 words)
Example sentences (20)
A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras.
A ring homomorphism is said to be an isomorphism if there exists an inverse homomorphism to f (i.
It is possible to have a rng homomorphism between (unital) rings that is not a ring homomorphism.
Moreover, every homomorphism between Lie algebras lifts to a unique homomorphism between the corresponding simply connected Lie groups.
Moreover, every Lie group homomorphism induces a homomorphism between the corresponding Lie algebras.
Not every semigroup homomorphism is a monoid homomorphism, since it may not map the identity to the identity of the target monoid, even though the element it maps the identity to will be an identity of the image of the mapping.
Since is a homomorphism that has an inverse that is also a homomorphism, is an isomorphism of groups.
Two Lie groups are called isomorphic if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism.
Types of group homomorphism ;Monomorphismmain: A group homomorphism that is injective (or, one-to-one); i.e., preserves distinctness.
Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms.
A group homomorphism between two groups "preserves the group structure" in a precise sense – it is a "process" taking one group to another, in a way that carries along information about the structure of the first group into the second group.
Any bijective ring homomorphism is a ring isomorphism.
Any such homomorphism is called a (permutation) representation of G on M. For any permutation group, the action that sends (g, x) → g(x) is called the natural action of G on M. This is the action that is assumed unless otherwise indicated.
A quasigroup homotopy from Q to P is a triple (α, β, γ) of maps from Q to P such that : for all x, y in Q. A quasigroup homomorphism is just a homotopy for which the three maps are equal.
A ring homomorphism between the same ring is called an endomorphism and an isomorphism between the same ring an automorphism.
A similar argument shows that the natural ring homomorphism from any commutative ring R to any one of its localizations is an epimorphism.
Conversely, the kernel of any semigroup homomorphism is a semigroup congruence.
Equivalently, it is a diffeomorphism which is also a group homomorphism.
Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
Every embedding is an injective homomorphism, but the converse holds only if the signature contains no relation symbols.
Common combinations with homomorphism
These word pairs occur most frequently in English texts:
- ring homomorphism 19×
- homomorphism is 17×
- group homomorphism 14×
- homomorphism from 14×
- homomorphism between 9×
- homomorphism of 8×
- is homomorphism 5×
- the homomorphism 5×
- homomorphism and 4×
- this homomorphism 4×