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homomorphism (plural homomorphisms)
- (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.
- 1997, Glen E. Bredon, Sheaf Theory, 2nd Edition, Springer, page 8,
- A homomorphism of presheaves is a collection of homomorphisms commuting with restrictions.
- 2003, Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, page 17,
- Definition 1.15. Let and be matrix Lie groups. A map from to is called a Lie group homomorphism if (1) is a group homomorphism and (2) is continuous.
- (biology) A similar appearance of two unrelated organisms or structures.
- (structure-preserving map between algebraic structures): automorphism, endomorphism, epimorphism, isomorphism, linear map, monomorphism
notion in mathematics
- Group homomorphism on Wikipedia.Wikipedia
- Ring homomorphism on Wikipedia.Wikipedia
- Linear map on Wikipedia.Wikipedia
- Algebra homomorphism on Wikipedia.Wikipedia
- Glossary of field theory#Homomorphisms on Wikipedia.Wikipedia
- Semigroup#Homomorphisms and congruences on Wikipedia.Wikipedia
- Homomrphism on Encyclopedia of Mathematics
- homomorphism on nLab