query: Quotient of a PID by a prime ideal
positive_passages.docid: 138114
positive_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 27916
negative_passages.text: Are the determinantal ideals prime?
negative_passages.docid: 111114
negative_passages.text: Prove that an ideal in $k[x,y]$ is a prime ideal
negative_passages.docid: 67342
negative_passages.text: Why does a minimal prime ideal consist of zerodivisors?
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 50809
negative_passages.text: Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
negative_passages.docid: 23099
negative_passages.text: Verifying that the ideal $(x^3-y^2)$ is prime
negative_passages.docid: 119056
negative_passages.text: If in a UFD every maximal ideal is principal then it is a PID
negative_passages.docid: 6507
negative_passages.text: Every prime ideal of height 1 in a UFD is principal
negative_passages.docid: 104784
negative_passages.text: On the grade of an ideal
negative_passages.docid: 44083
negative_passages.text: prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
negative_passages.docid: 149747
negative_passages.text: Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
negative_passages.docid: 83050
negative_passages.text: Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 1719
negative_passages.text: Ideals in the ring of Gaussian integers
negative_passages.docid: 81743
negative_passages.text: Prime ideals in $C[0,1]$
negative_passages.docid: 109199
negative_passages.text: Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$