query: Product of two irreducible affine varieties is irreducible.
positive_passages.docid: 20612
positive_passages.text: Is fibre product of varieties irreducible (integral)?
negative_passages.docid: 70537
negative_passages.text: Irreducible polynomials have distinct roots?
negative_passages.docid: 10627
negative_passages.text: When is $X^n-a$ is irreducible over F?
negative_passages.docid: 133312
negative_passages.text: Are these polynomials irreducible in $\mathbb{Q}[x]$?
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
negative_passages.docid: 127310
negative_passages.text: Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
negative_passages.docid: 74224
negative_passages.text: On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
negative_passages.docid: 116588
negative_passages.text: All polynomial parametric curves in $k^2$ are contained in affine algebraic varieties
negative_passages.docid: 64861
negative_passages.text: Intersection of open affines can be covered by open sets distinguished in *both*affines
negative_passages.docid: 76017
negative_passages.text: Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
negative_passages.docid: 28079
negative_passages.text: Do these definitions of irreducibility of algebraic sets coincide?
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
negative_passages.docid: 28658
negative_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 2043
negative_passages.text: $X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
negative_passages.docid: 142093
negative_passages.text: The closure of an irreducible subset of an irreducible space is irreducible.
negative_passages.docid: 66355
negative_passages.text: A sufficient condition for irreducibility of a polynomial in an extension field.