query: What is the kernel of $\varphi : R[u,v]\to R[x,1/x]$ defined by $\varphi(p(u,v))=p(x,1/x)$?
positive_passages.docid: 42552
positive_passages.text: Localisation is isomorphic to a quotient of polynomial ring
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 26665
negative_passages.text: When does the kernel of a function equal the image?
negative_passages.docid: 151400
negative_passages.text: Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$
negative_passages.docid: 15596
negative_passages.text: Identification of each tangent space $T_pV$ with $V$ itself?
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 83815
negative_passages.text: Identify the universal property of kernels
negative_passages.docid: 124844
negative_passages.text: Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
negative_passages.docid: 14830
negative_passages.text: A transformation of F[x]
negative_passages.docid: 66610
negative_passages.text: Finding a correspondence between $\{0,1\}^A$ and $\mathcal P(A)$
negative_passages.docid: 5802
negative_passages.text: Proving the universal mapping property for polynomial rings
negative_passages.docid: 87179
negative_passages.text: Why does this identity hold for Fejér Kernels?
negative_passages.docid: 67289
negative_passages.text: Continuity of the Characteristic Function of a RV
negative_passages.docid: 104413
negative_passages.text: Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
negative_passages.docid: 84021
negative_passages.text: How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?
negative_passages.docid: 44281
negative_passages.text: Proof of sum of kernels of concatenated vector
negative_passages.docid: 46746
negative_passages.text: How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?