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visits member for 2 years, 11 months
seen Dec 7 at 14:27

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.


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?
Mar
5
comment Monic irreducible polynomial over an integral domain
So..., if $f(x) \in D[x]$ is monic, then $f(x)$ is super primitive . Right?