query: Find Kernel of map $f:K[X,Y] \rightarrow K[T]$ defined by $f(X) = T^2, f(Y) = T^3$
positive_passages.docid: 143429
positive_passages.text: Kernel of ring homomorphism $k[X,Y] \rightarrow k[t^2, t^3]$
negative_passages.docid: 48990
negative_passages.text: Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
negative_passages.docid: 103019
negative_passages.text: Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
negative_passages.docid: 25260
negative_passages.text: Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
negative_passages.docid: 34234
negative_passages.text: Kernel of injective group homomorphism
negative_passages.docid: 32432
negative_passages.text: Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
negative_passages.docid: 102856
negative_passages.text: Intersection of kernels and linear dependence of functionals
negative_passages.docid: 49126
negative_passages.text: For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?
negative_passages.docid: 68006
negative_passages.text: Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
negative_passages.docid: 46622
negative_passages.text: Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.
negative_passages.docid: 153406
negative_passages.text: $[F(t):F(t^n)]=n$ where $t$ is trascendental
negative_passages.docid: 87179
negative_passages.text: Why does this identity hold for Fejér Kernels?
negative_passages.docid: 156858
negative_passages.text: Kernel of powers of a normal operator
negative_passages.docid: 27265
negative_passages.text: Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
negative_passages.docid: 39487
negative_passages.text: Zariski Tangent Space and $k[\varepsilon]/\varepsilon^2$
negative_passages.docid: 32443
negative_passages.text: Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$
negative_passages.docid: 359
negative_passages.text: Show that $\ker \hat{T} = \text{ann}(\text{range } T)$