self-homomorphism
[/sɛlf həˈmɔːrfɪzəm/]
nounpl: self-homomorphisms
automorfismo próprio / endomorfismo
1. In mathematics, a homomorphism from a mathematical structure to itself; an endomorphism that is also an automorphism
A self-homomorphism of a group G is a homomorphism from G to G that preserves the group structure.
Um automorfismo próprio de um grupo G é um homomorfismo de G em G que preserva a estrutura de grupo.
2. More broadly, any endomorphic mapping of an algebraic or mathematical object onto itself
The self-homomorphism of the vector space demonstrates how linear transformations can map vectors to themselves.
O automorfismo próprio do espaço vetorial demonstra como transformações lineares podem mapear vetores para si mesmos.
This is a specialized term used exclusively in academic mathematics and theoretical computer science. It is not part of everyday Portuguese or English vocabulary. The term is standardized internationally in mathematical literature, though the exact translation may vary slightly between Brazilian Portuguese, European Portuguese, and English-speaking regions. In Brazil, it is primarily encountered in university-level mathematics courses, particularly in abstract algebra and category theory.
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