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.
Synonyms / Sinônimos
generatorprimitive rootbasic elementfundamental element
Antonyms / Antônimos
composite elementderived elementcomplex element

Regional Variations

General Brazilian Portuguese
elemento primitivo
standard mathematical term used in universities and academic contexts
Portugal
elemento primitivo
same as Brazilian Portuguese; consistent across Portuguese-speaking academic communities
Academic English
elemento primitivo or raiz primitiva
raiz primitiva more commonly used for primitive roots in modular arithmetic contexts

Related Words

field extensioncyclic groupmultiplicative groupalgebraic elementirreducible polynomialminimal polynomial
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