query: Morphism between quotient polynomial rings
positive_passages.docid: 146334
positive_passages.text: Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
negative_passages.docid: 89313
negative_passages.text: Maximal ideals of polynomial rings in infinitely many variables
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 47086
negative_passages.text: Quotient rings and free modules
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 25383
negative_passages.text: Morphism between quotient sheaf ($K_{X}/\mathcal{O}_{X}$) and $\bigoplus_{x\in\mathcal{X}}i_{x,*}(K(X)/\mathcal{O}_{X,x})$
negative_passages.docid: 149856
negative_passages.text: Image of ring homomorphism is a subring
negative_passages.docid: 32172
negative_passages.text: Homomorphisms of graded modules
negative_passages.docid: 30327
negative_passages.text: $\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 82559
negative_passages.text: Showing two ring homomorphisms that agree on the integers must agree on the rationals
negative_passages.docid: 130814
negative_passages.text: Quotient of semi-simple rings
negative_passages.docid: 93632
negative_passages.text: Existence of a ring homomorphism implies characteristic divisibility
negative_passages.docid: 48818
negative_passages.text: Homomorphism of local rings
negative_passages.docid: 77862
negative_passages.text: Question about fields and quotients of polynomial rings