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27 votes
Accepted

if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian

16 votes

Can a non-local ring have only two prime ideals?

11 votes
Accepted

If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)

8 votes
Accepted

Is any UFD also a PID?

8 votes
Accepted

Krull dimension of Noetherian local rings is finite

7 votes

How to learn commutative algebra?

6 votes
Accepted

Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal

6 votes
Accepted

"Subtracting" sets question

5 votes
Accepted

How do ideal quotients behave with respect to localization?

5 votes

Module homomorphism question

5 votes

convergence of $\int_a^b \frac{1}{x^2} dx$

5 votes

Proving that two quotient modules are isomorphic

5 votes
Accepted

What does ''$\le$'' mean here?

5 votes

Does set difference distribute over set intersection?

4 votes
Accepted

Two definitions of Jacobson Radical

4 votes
Accepted

Is $\frac{n}{3}! = (\frac{1}{3})^n n!$

4 votes

The quotient of product of rings

4 votes

Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit

4 votes
Accepted

A finite sum of $1$ equals $0$ in a field with finitely many elements.

4 votes
Accepted

$A$ is a commutative ring, $P$ is a prime ideal. Prove $A_P$ is local ring

4 votes
Accepted

Local Noetherian domain of dimension one with principal maximal ideal

4 votes

Why does $p(a)=0$ imply $(x-a) \mid p$?

4 votes

How to go about this proof for non zero polynomials.

4 votes
Accepted

radical membership and ideal membership

4 votes
Accepted

The "general algorithm" for primary decomposition

4 votes
Accepted

Image of ring homomorphism is a subring

4 votes

What does Hom(M,N) mean? Atiyah Macdonald proposition 2.9

3 votes
Accepted

Number of generators of an ideal in $k[x,y]$

3 votes
Accepted

What does $(0:x)$ mean?

3 votes

Set Interview Question, Any Creative Way to solve?

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