User user26857

28 votes

Nontrivial theorems with trivial proofs

answered Nov 30, 2015 at 17:41

16 votes

Is a domain all of whose localizations are noetherian itself noetherian ?

answered Nov 2, 2019 at 19:16

9 votes

Accepted

Radical generation of ideals in Noetherian rings

answered Nov 13, 2012 at 2:01

9 votes

Hilbert's Nullstellensatz on polynomials with integer coefficients

answered Feb 2, 2013 at 2:29

5 votes

Errata for Atiyah–Macdonald

answered Apr 11, 2014 at 15:34

4 votes

Strongly Noetherian property. When is the tensor $A\otimes_{k}B$ Noetherian for Noetherian rings $A$ and $B$?

answered Nov 12, 2012 at 19:00

3 votes

Is a Laskerian ring coherent

answered Nov 17, 2015 at 11:01

2 votes

Canonical module of rees algebra

answered Feb 14, 2015 at 8:47

2 votes

Accepted

Prime ideal ramified in extension if and only if certain polynomial divides another one?

answered Mar 29, 2016 at 16:22

2 votes

Accepted

Are f.g. projective modules free over total quotient ring of a reduced non-noetherian commutative ring

answered Feb 21, 2013 at 11:47

2 votes

Accepted

If the quotient of a local ring is regular, does that imply that the original ring must be regular?

answered Jul 7, 2013 at 8:11

2 votes

Accepted

vanishing of local cohomology $H^2_{(x,y)}\left(\frac{\Bbb Z[x,y]}{(5x+4y)}\right)=0$

answered Dec 8, 2012 at 17:55

2 votes

Accepted

Vanishing of Tor

answered Jan 11, 2013 at 20:26

1 vote

Is a polynomial ring integral over this subring ?

answered Nov 22, 2012 at 1:41

1 vote

Homogeneous ideal and its system of generators

answered Oct 18, 2012 at 9:25

1 vote

transcendence degree of subring of polynomial ring

answered Oct 19, 2012 at 19:42

1 vote

Accepted

Filter-regular sequence and regularity

answered Oct 23, 2012 at 10:35

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17 Answers

Nontrivial theorems with trivial proofs

Is a domain all of whose localizations are noetherian itself noetherian ?

Radical generation of ideals in Noetherian rings

Hilbert's Nullstellensatz on polynomials with integer coefficients

Errata for Atiyah–Macdonald

Strongly Noetherian property. When is the tensor $A\otimes_{k}B$ Noetherian for Noetherian rings $A$ and $B$?

Is a Laskerian ring coherent

Canonical module of rees algebra

Prime ideal ramified in extension if and only if certain polynomial divides another one?

Are f.g. projective modules free over total quotient ring of a reduced non-noetherian commutative ring

If the quotient of a local ring is regular, does that imply that the original ring must be regular?

vanishing of local cohomology $H^2_{(x,y)}\left(\frac{\Bbb Z[x,y]}{(5x+4y)}\right)=0$

Vanishing of Tor

Is a polynomial ring integral over this subring ?

Homogeneous ideal and its system of generators

transcendence degree of subring of polynomial ring

Filter-regular sequence and regularity