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visits member for 3 years
seen Jan 12 at 15:00

My interesting is about commutative algebra, homological algebra, coding theory and all topic related algebra, for exmaple, algebraic geometry, algebraic number theory, algebraic topology and their applications.

This days, I focus on studying and learning in the following topic:

  1. Much more commutative algebra and homological algebra, for example, Cohen-Macaulay rings, Koszul complexes and its applications.

  2. Algebraic number theory, finite fields and information theory.

  3. Applications of algebraic geometry and topology in information theory.


Jan
12
accepted Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?
Dec
7
comment Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?
But the formula $[k(a,b):k][k(a) \cap k(b):k] \leq [k(a):k][k(b):k]$ is true. Right? (by my computation...)
Dec
7
comment Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?
Oh! I see! Thank you very much! (so... I think I need to find another way to correct my note...)
Dec
7
asked Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?
Oct
28
awarded  Popular Question
Oct
7
awarded  Popular Question
Sep
24
awarded  Autobiographer
Sep
3
comment An Estimation for Multiple Points in Fulton's Curve Book
Aha! I forgot that the dimension of the empty set is -1, not zero. Sorry, I was confused with the definition dimension of linear subvarieties in affine case (since $\mathcal{V}_p(X_1, \dots, X_n, X_{n+1}) = \emptyset$)! I think I have no question about this proof now...
Sep
2
revised An Estimation for Multiple Points in Fulton's Curve Book
added 2 characters in body; edited tags
Sep
1
revised An Estimation for Multiple Points in Fulton's Curve Book
added 4 characters in body
Sep
1
asked An Estimation for Multiple Points in Fulton's Curve Book
Jul
2
awarded  Curious
May
12
comment How to show that $(Y- X^2, Z - X^3) \subseteq k[X,Y,Z]$ is a prime ideal?
Thanks a lot! :)
May
12
accepted How to show that $(Y- X^2, Z - X^3) \subseteq k[X,Y,Z]$ is a prime ideal?
May
12
asked How to show that $(Y- X^2, Z - X^3) \subseteq k[X,Y,Z]$ is a prime ideal?
Mar
10
accepted Monic irreducible polynomial over an integral domain
Mar
5
revised Monic irreducible polynomial over an integral domain
added 251 characters in body
Mar
5
comment Monic irreducible polynomial over an integral domain
Ah!!!!!!!! Dear all: for the second question, I may find a error! Because there are 2 assumptions of $f_1(y)$, I require that $f_1$ must be monic and have minimal degree... But I don't know $r(y)$ and $r'(y)$ are monic or not!!!!!!!
Mar
5
comment Monic irreducible polynomial over an integral domain
Dear @Bill: does this criterion have a name? or where could I find this criterion? (some papers, text books...) Thank you very much!
Mar
5
comment Monic irreducible polynomial over an integral domain
Dear @Bill: Yeah~ I see. But I just want to insure that any monic polynomial in $D[x]$ is super primitive. Is this statement correct?