generating set
[/ˈdʒɛnəreɪtɪŋ sɛt/]
nounpl: generating sets
conjunto gerador
1. In algebra and group theory, a subset of a mathematical structure from which all elements of the structure can be obtained through the application of certain operations
The set {2, 3} is a generating set for the integers under addition.
O conjunto {2, 3} é um conjunto gerador para os inteiros sob adição.
2. A set of elements whose combinations or applications produce all elements in a given group, ring, or other algebraic structure
In linear algebra, a generating set of a vector space is a set of vectors that span the entire space.
Em álgebra linear, um conjunto gerador de um espaço vetorial é um conjunto de vetores que gera todo o espaço.
3. The minimal generating set is called a basis when the elements are linearly independent
Finding a minimal generating set is important for understanding the structure of the group.
Encontrar um conjunto gerador minimal é importante para entender a estrutura do grupo.
This is a technical mathematical term used primarily in academic and research contexts. It is universal across English-speaking and Portuguese-speaking mathematical communities, with identical terminology in both Brazilian Portuguese and European Portuguese. The term is fundamental in abstract algebra courses at the university level.
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