query: A non-UFD where prime=irreducible
positive_passages.docid: 148434
positive_passages.text: Ring where irreducibles are primes which is not an UFD
negative_passages.docid: 113863
negative_passages.text: The non-existence of non-principal ultrafilters in ZF
negative_passages.docid: 141418
negative_passages.text: When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
negative_passages.docid: 53525
negative_passages.text: Infiniteness of non-twin primes.
negative_passages.docid: 3037
negative_passages.text: Integral domain without unity has prime characteristic?
negative_passages.docid: 135102
negative_passages.text: How do the definitions of "irreducible" and "prime" elements differ?
negative_passages.docid: 19968
negative_passages.text: Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
negative_passages.docid: 24988
negative_passages.text: Prove there exists $m > 2010$ such that $f(m)$ is not prime
negative_passages.docid: 142707
negative_passages.text: Intermediate fields of a finite field extension that is not separable
negative_passages.docid: 34807
negative_passages.text: Localization at finitely many minimal prime ideals
negative_passages.docid: 41693
negative_passages.text: Use irreducible fibers to show $X$ is irreducible
negative_passages.docid: 86724
negative_passages.text: Example of a non-zero module that has no associated primes
negative_passages.docid: 133617
negative_passages.text: Relatively prime property verification
negative_passages.docid: 144592
negative_passages.text: how to prove the existence and uniqueness of the prime factorization of any natural number.
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 16592
negative_passages.text: Irreducible polynomial which is reducible modulo every prime
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition