Commit 2025-06-17 13:09 d9d3b4ca
View on Github →feat(RingTheory/Polynomial/ContentIdeal): more theorems (#25960)
We prove more facts about contentIdeal
.
For instance we prove that
(p * q).contentIdeal $\le$ p.contentIdeal * q.contentIdeal $\le$ (p * q).contentIdeal.radical
which implies the following result, often called Gauss' Lemma
Polynomial.contentIdeal_mul_eq_top_of_contentIdeal_eq_top {p q : R[X]} (hp : p.contentIdeal = ⊤)
(hq : q.contentIdeal = ⊤) : (p * q).contentIdeal = ⊤
Zulip discussion here