Nota: A tradução desta entrada está atualmente em revisão de qualidade, portanto parte do conteúdo é exibida temporariamente apenas em inglês.
Este verbete ainda não foi traduzido para o seu idioma, portanto o original é exibido abaixo.
endomorphism
This term is used exclusively within the specialized domains of category theory, abstract algebra, and linear algebra. It describes a mapping where the domain and codomain are the same object, creating a closed loop of transformation that allows for the study of internal symmetries and structural invariants.
Because it refers to a specific mathematical entity, it is treated as a standard countable noun. In professional mathematical discourse, it is frequently paired with the term ring to describe the set of all such mappings under addition and composition.
Meanings
Examples
An endomorphism is a morphism from a mathematical object to itself.
Is this specific mapping an endomorphism or a general homomorphism?
I need to determine if this linear transformation is an endomorphism.
The set of all endomorphisms of a module forms a ring.
Wait, if the domain and codomain are the same, then it must be an endomorphism.
The professor explained the properties of an endomorphism on a vector space.
Every automorphism is by definition an endomorphism.
Every automorphism is by definition an endomorphism.
Let us consider a simple endomorphism of the group G.
I wonder if this particular endomorphism is invertible.
I wonder if this particular endomorphism is invertible.