1,112 reputation
313
bio website
location Hanoi
age 30
visits member for 2 years, 7 months
seen Apr 3 at 11:13

I am interested in commutative algebra, especially, local cohomology and characteristic $p$ method.


Mar
1
awarded  Self-Learner
Feb
28
comment Dimension of a ring after localization
Example $u = 1 + X$ and $v = 1 + X^2$ we have $u - v = X - X^2 = X(1 -X)$ is unit in $T_S$ since both $X$ and $1-X$ are units in $T_S$.
Feb
28
revised Dimension of a ring after localization
added 42 characters in body
Feb
28
comment Dimension of a ring after localization
Thanks you Mahdi! I accepted your answer.
Feb
28
accepted Dimension of a ring after localization
Feb
28
answered Dimension of a ring after localization
Feb
28
comment Dimension of a ring after localization
Dear Fred, I do not have that paper. Could you please sent it for me. I think I can prove it.
Feb
27
comment Dimension of a ring after localization
I only known Countable Prime Avoidance Lemma for complete local ring before. Thanks you very much for the new form. But the ring in my question do not have this assumption.
Feb
27
comment Dimension of a ring after localization
Thanks you Fred. But in my question we do not assume that $R/\mathfrak{m}$ is uncountable.
Feb
27
comment Dimension of a ring after localization
I know Countable Prime Avoidance Lemma. But I do not know how to apply it for my question. Could you give a detail answer.
Feb
26
asked Dimension of a ring after localization
Feb
7
awarded  Notable Question
Oct
26
answered Colon property of Gorenstein rings
Oct
26
comment Colon property of Gorenstein rings
I work with all parameter ideals
Oct
25
comment Colon property of Gorenstein rings
@ Youngsu: I have proved that the ring satisfying the question must be $F$-regular.
Oct
24
comment Colon property of Gorenstein rings
I think so. I have just see this paper of Wenliang Zhang (arxiv.org/abs/0709.0943), the condition (C) in this paper is much similar to my question. He consider colon property for all ideals. So I think that ring satisfying my question may be regular of $F$-regualar. Do you have any example of non-regular ring for my question?
Oct
23
comment Colon property of Gorenstein rings
Thank you. Do you have any example with $R$ is reduce.
Oct
23
accepted Colon property of Gorenstein rings
Oct
22
asked Colon property of Gorenstein rings
Oct
8
comment Bernstein-Sato polynomial (one variable)
Thanks you. Based on your answer I think we can give an explicit answer for some questions of Lyubeznik in this paper ams.org/journals/proc/1997-125-07/S0002-9939-97-03774-X in the case one variable.