query: Irreducible element in $D$ is irreducible in $D[x]$
positive_passages.docid: 17670
positive_passages.text: If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension
negative_passages.docid: 114198
negative_passages.text: Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
negative_passages.docid: 134055
negative_passages.text: Some irreducible character separates elements in different conjugacy classes
negative_passages.docid: 152109
negative_passages.text: In a UFD if $x$ is irreducible, then $(x)$ is prime
negative_passages.docid: 55432
negative_passages.text: Infinite distinct factorizations into irreducibles for an element
negative_passages.docid: 344
negative_passages.text: Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
negative_passages.docid: 115782
negative_passages.text: Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
negative_passages.docid: 121714
negative_passages.text: Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
negative_passages.docid: 102871
negative_passages.text: $\langle r\rangle$ maximal $\iff r$ irreducible
negative_passages.docid: 120673
negative_passages.text: Irreducible fibers of a closed subset implies irreducibility
negative_passages.docid: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
negative_passages.docid: 141792
negative_passages.text: Slick proof the determinant is an irreducible polynomial
negative_passages.docid: 93291
negative_passages.text: Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 140550
negative_passages.text: Irreducible element iff prime norm in Gaussian integers?
negative_passages.docid: 80188
negative_passages.text: There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$