homomorphism

1. A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.

   A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.

   Homomorphismus

   гомоморфи́змgomomorfízm

   гомоморфізмhomomorfizm

2. A similar appearance of two unrelated organisms or structures, as for example with fish and whales.

1. In algebra a monomorphism is an injective homomorphism.

   В алгебрі мономорфізм - це ін'єктивний гомоморфізм. — deniko

   ruВ алгебре мономорфизм — это инъективный гомоморфизм. — arseniiv

   deIn der Algebra ist ein Monomorphismus ein injektiver Homomorphismus. — MUIRIEL

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2. One must not confuse homomorphism with homeomorphism.

   ruНе следует путать гомоморфизм с гомеоморфизмом. — odexed

   deMan darf nicht Homomorphismen mit Homöomorphismen verwechseln. — MUIRIEL

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3. The kernel of a group homomorphism always contains the neutral element.

   ruЯдро гомоморфизма групп всегда содержит нейтральный элемент. — al42and

   deDer Kern eines Gruppenhomomorphismus enthält immer das neutrale Element. — MUIRIEL

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regular