primitive polynomial

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|algebra|ring theory}} A [[polynomial]] over an [[integral domain]] ''R'' such that no [[noninvertible]] element of ''R'' divides all its [[coefficient]]s at once; {{lb|en|more specifically}} a polynomial over a [[GCD domain]] ''R'' such that the [[greatest common divisor]] of its coefficients equals 1.
2. {{lb|en|algebra|field theory}} A polynomial over a given finite [[field]] whose roots are [[primitive element]]s; ''especially'', the [[minimal polynomial]] of a primitive element of said finite field.

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