Polynomial ring

English

Noun

1. Template:Lb A Template:L (which is also a commutative algebra), denoted K[X], formed from the set of Template:L (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.
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Usage notes

• $K[X]$ is called the polynomial ring (or ring of polynomials) in $X$ over $K$.
• The notation $K[X_1,X_2,\dots ,X_n]$ is standardly used for the case of a polynomial ring in multiple variables.
  • It is possible to speak of a polynomial ring in an infinite set of variables, provided it is assumed that any individual polynomial depends only on a finite number of variables.

Synonyms

• Template:Sense Template:L, Template:L

Hypernyms

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Derived terms

• Template:L (= Template:L)

Translations

• Italian: Template:T
• Polish: Template:T

See also

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Further reading

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• Ring of polynomials on Template:W