query: difference between irreducible element in a ring and integral domain
positive_passages.docid: 155532
positive_passages.text: difference between irreducible element and irreducible polynomial
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring
negative_passages.docid: 157420
negative_passages.text: Question about Subrings and integraly closed
negative_passages.docid: 8317
negative_passages.text: Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
negative_passages.docid: 20612
negative_passages.text: Is fibre product of varieties irreducible (integral)?
negative_passages.docid: 93621
negative_passages.text: Prove that $\mathbb{Z}[\omega]$ is an integral domain
negative_passages.docid: 45523
negative_passages.text: Can the product of two non invertible elements in a ring be invertible?
negative_passages.docid: 84149
negative_passages.text: Prove that an infinite ring with finite quotient rings is an integral domain
negative_passages.docid: 134458
negative_passages.text: Isomorphisms preserving integral domains and fields
negative_passages.docid: 22544
negative_passages.text: Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
negative_passages.docid: 135152
negative_passages.text: Non-UFD integral domain such that prime is equivalent to irreducible?
negative_passages.docid: 19838
negative_passages.text: Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 102914
negative_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 38190
negative_passages.text: Discriminant of a monic irreducible integer polynomial vs. discriminant of its splitting field
negative_passages.docid: 73344
negative_passages.text: Definition of irreducible polynomial via the units of an integral domain.
negative_passages.docid: 139463
negative_passages.text: Commutative integral domain does not finitely generate its field of fractions