query: Affine $K$-algebra is Hilbert ring!?
positive_passages.docid: 150206
positive_passages.text: Every finitely generated algebra over a field is a Jacobson ring
negative_passages.docid: 118911
negative_passages.text: Classifying Unital Commutative Rings of Order $p^2$
negative_passages.docid: 82609
negative_passages.text: Ring such that $x^4=x$ for all $x$ is commutative
negative_passages.docid: 464
negative_passages.text: Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
negative_passages.docid: 79460
negative_passages.text: Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra.
negative_passages.docid: 75520
negative_passages.text: If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
negative_passages.docid: 78945
negative_passages.text: Are the rings $k[[t^3,t^4,t^5]]$ and $k[[t^4,t^5,t^6]]$ Gorenstein? (Matsumura, Exercise 18.8)
negative_passages.docid: 22610
negative_passages.text: Polynomial rings in infinitely indeterminants
negative_passages.docid: 29756
negative_passages.text: Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 126331
negative_passages.text: Associative ring with identity, inverses, divisors of zero and Artinianity
negative_passages.docid: 116883
negative_passages.text: About ideals in a ring which is a $k$ vector space
negative_passages.docid: 8587
negative_passages.text: What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 155604
negative_passages.text: Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
negative_passages.docid: 146714
negative_passages.text: Rees algebra of a monomial ideal
negative_passages.docid: 27096
negative_passages.text: Hilbert polynomial of an hypersurface in projective space