homomorphism
Sign in to saveIn algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: () meaning "same" and () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German meaning "similar" to meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).
Article
15 sectionsContents
- Definition
- Examples
- Special homomorphisms
- Isomorphism
- Endomorphism
- Automorphism
- Monomorphism
- Epimorphism
- Kernel
- Relational structures
- Formal language theory
- See also
- Notes
- Citations
- References
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: () meaning "same" and () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German meaning "similar" to meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).
Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra.