If R is a Noetherian ring, is it true that there exists an integer N such that every ideal of R is generated by at most N elements?
107002
Noetherian ring whose ideals have arbitrarily large number of generators
63736
Every radical ideal in a Noetherian ring is a finite intersection of primes
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
29019
Ideals in direct product of rings
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
22544
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.
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
3327
Height and minimal number of generators of an ideal
40975
Quotient of the ring of integers of a number field by a prime ideal
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
68202
Must an ideal generated by an irreducible element be a maximal ideal?
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
49854
Ideals in polynomial rings generated by linear polynomials
21538
Can a ring of positive characteristic have infinite number of elements?
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
74314
Noetherian ring and the same prime divisors