query: Showing  =nZ is a prime ideal of Z IFF n is a prime
positive_passages.docid: 146304
positive_passages.text: prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 16602
negative_passages.text: Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 135586
negative_passages.text: Prove that the preimage of a prime ideal is also prime.
negative_passages.docid: 99715
negative_passages.text: Proper ideal and units proof
negative_passages.docid: 72640
negative_passages.text: $(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
negative_passages.docid: 7899
negative_passages.text: Show that if $p$ is prime then $\Bbb Z_p$ is a field
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 111114
negative_passages.text: Prove that an ideal in $k[x,y]$ is a prime ideal
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
negative_passages.docid: 17247
negative_passages.text: Localisation and prime ideals
negative_passages.docid: 129302
negative_passages.text: Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal