Gauss's Lemma on Primitive Polynomials over Ring

Theorem

Let $R$ be a commutative ring with unity.

Let $f, g \in R \sqbrk X$ be primitive polynomials.

This article, or a section of it, needs explaining. In particular: Definition:Primitive Polynomial over Ring You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

Then $f g$ is primitive.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Source of Name

This entry was named for Carl Friedrich Gauss.