primitive element
[PRIM-uh-tiv EL-uh-munt]
nounpl: primitive elements
elemento primitivo
1. In algebra and field theory, an element that generates a given field extension or cyclic group through its powers or multiples
In the field extension Q(√2) over Q, √2 is a primitive element.
Na extensão de corpo Q(√2) sobre Q, √2 é um elemento primitivo.
2. In number theory, a generator of the multiplicative group of integers modulo p (primitive root)
3 is a primitive element modulo 7 because its powers generate all non-zero residues.
3 é um elemento primitivo módulo 7 porque suas potências geram todos os resíduos não-nulos.
3. In computer science and formal languages, a basic symbol or token that cannot be decomposed further
In programming languages, variables and literals are primitive elements of the grammar.
Em linguagens de programação, variáveis e literais são elementos primitivos da gramática.
This is primarily a mathematical and scientific term used in academic and research contexts. It is consistently used across English and Portuguese-speaking mathematics communities without significant regional variation. The term is essential in abstract algebra, cryptography, and number theory courses at the university level.
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