query: Structure of Quotient Ring
positive_passages.docid: 8434
positive_passages.text: Order of $\mathbb{Z}[i]/(1+i)$
negative_passages.docid: 113512
negative_passages.text: Characteristic of nonzero commutative rings with unity
negative_passages.docid: 101151
negative_passages.text: Values of c for which the given quotient ring is a field.
negative_passages.docid: 54585
negative_passages.text: Order of some quotient ring of Gaussian integers
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 29359
negative_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 61526
negative_passages.text: An exercise about nilpotent quotient groups
negative_passages.docid: 97999
negative_passages.text: Explain these ring isomorphisms
negative_passages.docid: 65637
negative_passages.text: Squares in Polynomial Quotient Ring $ (\mathbb{Z}/2)[x] /(x^{17} - 1) $
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 105322
negative_passages.text: Computing the quotient of SL(2,Z) by its commutator subgroup
negative_passages.docid: 148369
negative_passages.text: Quotient groups of D10
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
negative_passages.docid: 78006
negative_passages.text: What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
negative_passages.docid: 27704
negative_passages.text: Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
negative_passages.docid: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$