Definition:Primitive Polynomial (Ring Theory)
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Let $f \in \Q \sqbrk X$ be such that:
- $\cont f = 1$
where $\cont f$ is the content of $f$.
Then $f$ is described as primitive.
Also defined as
From Polynomial has Integer Coefficients iff Content is Integer it follows that, if $f$ is a primitive polynomial, then:
- $f \in \Z \sqbrk X$
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 31$. Polynomials with Integer Coefficients
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: primitive polynomial