Homomorphism example sentences

"Homomorphism" Example Sentences

1. The notion of a homomorphism between two algebraic structures is an important one in abstract algebra.
2. The homomorphism between two groups is a mapping that preserves the group structure.
3. Homomorphisms are used to define the notion of isomorphism between two algebraic structures.
4. It is possible to define a homomorphism between two groups that is not an isomorphism.
5. Every homomorphism from a group to itself is an automorphism.
6. A homomorphism between two vector spaces is a linear transformation that preserves the vector space structure.
7. A homomorphism between two rings is a mapping that preserves the ring structure.
8. A homomorphism between two fields is a mapping that preserves the field structure.
9. A homomorphism between two lattices is a mapping that preserves the lattice structure.
10. A homomorphism between two modules is a mapping that preserves the module structure.
11. A homomorphism between two algebras is a mapping that preserves the algebra structure.
12. A homomorphism between two topological spaces is a mapping that preserves the topological structure.
13. A homomorphism between two groups is a mapping that preserves the group multiplication.
14. A homomorphism between two rings is a mapping that preserves the ring operations.
15. A homomorphism between two fields is a mapping that preserves the field operations.
16. A homomorphism between two lattices is a mapping that preserves the lattice operations.
17. A homomorphism between two modules is a mapping that preserves the module operations.
18. A homomorphism between two algebras is a mapping that preserves the algebra operations.
19. A homomorphism between two topological spaces is a mapping that preserves the topological properties.
20. A homomorphism between two groups is a mapping that preserves the group identity.
21. A homomorphism between two rings is a mapping that preserves the ring identity.
22. A homomorphism between two fields is a mapping that preserves the field identity.
23. A homomorphism between two lattices is a mapping that preserves the lattice identity.
24. A homomorphism between two modules is a mapping that preserves the module identity.
25. A homomorphism between two algebras is a mapping that preserves the algebra identity.
26. A homomorphism between two topological spaces is a mapping that preserves the topological identity.
27. Any homomorphism between two groups is necessarily injective or surjective.
28. Any homomorphism between two rings is necessarily injective or surjective.
29. Any homomorphism between two fields is necessarily injective or surjective.
30. Any homomorphism between two lattices is necessarily injective or surjective.
31. Any homomorphism between two modules is necessarily injective or surjective.
32. Any homomorphism between two algebras is necessarily injective or surjective.
33. Any homomorphism between two topological spaces is necessarily injective or surjective.
34. A homomorphism between two groups is an injective mapping if and only if it is an isomorphism.
35. A homomorphism between two rings is an injective mapping if and only if it is an isomorphism.
36. A homomorphism between two fields is an injective mapping if and only if it is an isomorphism.
37. A homomorphism between two lattices is an injective mapping if and only if it is an isomorphism.
38. A homomorphism between two modules is an injective mapping if and only if it is an isomorphism.
39. A homomorphism between two algebras is an injective mapping if and only if it is an isomorphism.
40. A homomorphism between two topological spaces is an injective mapping if and only if it is an isomorphism.