query: Why can a field not be used to make a quotient ring?
positive_passages.docid: 23641
positive_passages.text: Quotient ring of field is zero or itself.
negative_passages.docid: 133495
negative_passages.text: Example of a ring without Invariant Basis Property
negative_passages.docid: 24247
negative_passages.text: Ring Inside an Algebraic Field Extension
negative_passages.docid: 121643
negative_passages.text: Why isn't the zero ring the field with one element?
negative_passages.docid: 148118
negative_passages.text: Prove that field of complex numbers cannot be equipped with an order relation
negative_passages.docid: 151423
negative_passages.text: Is there a nice description of the field of fractions of the ring of polynomials with integer coefficients?
negative_passages.docid: 119305
negative_passages.text: Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
negative_passages.docid: 3129
negative_passages.text: A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
negative_passages.docid: 84751
negative_passages.text: How can it be possible to localize a ring at a set with zero divisors?
negative_passages.docid: 21079
negative_passages.text: Why must a field whose a group of units is cyclic be finite?
negative_passages.docid: 138911
negative_passages.text: Is $\mathbb R^2$ a field?
negative_passages.docid: 46047
negative_passages.text: Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
negative_passages.docid: 108408
negative_passages.text: Example of quotient mapping that is not open
negative_passages.docid: 84315
negative_passages.text: Why can't polynomials have negative exponents or division by a variable
negative_passages.docid: 105913
negative_passages.text: Calculations in quotient rings
negative_passages.docid: 98818
negative_passages.text: Quotient ring of a localization of a ring
negative_passages.docid: 101151
negative_passages.text: Values of c for which the given quotient ring is a field.