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Pronunciation varies by accent · noun
(algebra) 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.
1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54, This motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates.
A homomorphism of presheaves h#58;A#92;rightarrowB is a collection of homomorphisms h#95;U#58;A(U)#92;rightarrowB(U) commuting with restrictions.
Definition 1.15. Let G and H be matrix Lie groups. A map #92;Phi from G to H is called a Lie group homomorphism if (1) #92;Phi is a group homomorphism and (2) #92;Phi is continuous.
Use homœomorphism when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Homœomorphism means (algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.
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