noun

homomorphism

hoh-moh-MOR-fiz-uhm

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Homomorphism (noun) means In algebra, a map between two structures of the same kind, such as groups or rings, that preserves how their operations work. Example: “A group homomorphism always sends the identity element to the identity element of the other group.”

noun

mathematics In algebra, a map between two structures of the same kind, such as groups or rings, that preserves how their operations work.

"A group homomorphism always sends the identity element to the identity element of the other group."

"Mathematicians check whether a function is a homomorphism by testing whether it preserves the structure's operations."

"The map turned out to be a ring homomorphism between the two rings."

biology In biology, a similar appearance shared by two organisms or structures that are not closely related.

"The similar body shapes of fish and whales are often given as an example of homomorphism rather than shared ancestry."

"Biologists sometimes describe matching traits in unrelated species as homomorphism."

"The two insects show a striking homomorphism despite belonging to different families."

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How to use homomorphism

Learner’s notes

In plain EnglishIt's a way two things share the same underlying structure or shape, whether in maths or biology.

When to use it

Homomorphism is a specialist term, used mainly in mathematics and, separately, in biology.

Memory tip

In maths, use isomorphism instead of homomorphism only when you know the map can be reversed.

Trace the full origin ↓

Easily confused with

isomorphism morphism →

Common pairings

group homomorphism ring homomorphism structure-preserving map algebra homomorphism

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C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

Test yourself on “homomorphism” A quick quiz — meaning, synonyms & usage →

Fill the gap

Can you complete this real example?

A group _____ always sends the identity element to the identity element of the other group.

Etymology

Homomorphism is formed by combining homo-, meaning 'same', with morphism, a term for a structure-preserving map.

Rhymes for homomorphism

morphism polymorphism anthropomorphism

See all rhymes for homomorphism →

Frequently asked questions

What does homomorphism mean in maths?

It's a map between two algebraic structures, such as groups or rings, that preserves the way their operations work.

Is a homomorphism the same as an isomorphism?

Not quite: an isomorphism is a homomorphism that can also be reversed, so every isomorphism is a homomorphism but not every homomorphism is an isomorphism.

What does homomorphism mean in biology?

It refers to two organisms or structures that look alike even though they are not closely related, such as the similar shapes of fish and whales.

What is the meaning of homomorphism?

"homomorphism" (noun) means in algebra, a map between two structures of the same kind, such as groups or rings, that preserves how their operations work.