query: How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
positive_passages.docid: 3327
positive_passages.text: Height and minimal number of generators of an ideal
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 6646
negative_passages.text: A (non-artificial) example of a ring without maximal ideals
negative_passages.docid: 18406
negative_passages.text: An ideal whose radical is maximal is primary
negative_passages.docid: 74150
negative_passages.text: Problem on the number of generators of some ideals in $k[x,y,z]$
negative_passages.docid: 87382
negative_passages.text: Non-invertible elements form an ideal
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
negative_passages.docid: 60391
negative_passages.text: Ideal Generated by Three Elements in Polynomial Ring
negative_passages.docid: 92519
negative_passages.text: ideal behind Maximal ideals are Prime ideals
negative_passages.docid: 103830
negative_passages.text: Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal
negative_passages.docid: 252
negative_passages.text: Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
negative_passages.docid: 154239
negative_passages.text: Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
negative_passages.docid: 78455
negative_passages.text: Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements