query: Why is it called a ring, a field?
positive_passages.docid: 79641
positive_passages.text: Why are rings called rings?
negative_passages.docid: 24556
negative_passages.text: What is a field, really?
negative_passages.docid: 86234
negative_passages.text: Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
negative_passages.docid: 551
negative_passages.text: Why is a finite integral domain always field?
negative_passages.docid: 6646
negative_passages.text: A (non-artificial) example of a ring without maximal ideals
negative_passages.docid: 148192
negative_passages.text: In a field that is the direct product of two fields, why isn't it a field?
negative_passages.docid: 34990
negative_passages.text: Ring homomorphism defined on a field
negative_passages.docid: 76813
negative_passages.text: The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
negative_passages.docid: 125661
negative_passages.text: Two problems about rings.
negative_passages.docid: 70610
negative_passages.text: Why is ring addition commutative?
negative_passages.docid: 107605
negative_passages.text: Determining the characteristic of a field
negative_passages.docid: 85961
negative_passages.text: Is the ring and semi-ring definition of algebra and set linked?
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 22702
negative_passages.text: If Earth had rings?
negative_passages.docid: 4507
negative_passages.text: Localization of a ring which is not a domain
negative_passages.docid: 38817
negative_passages.text: Why is the ring of matrices over a field simple?
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