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visits member for 2 years, 7 months
seen Jul 28 at 20:58

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.


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?
Mar
5
revised Monic irreducible polynomial over an integral domain
added 37 characters in body
Mar
5
asked Monic irreducible polynomial over an integral domain
Mar
3
asked A question in Chapter III.4 of Dino Lorenzini's “An Invitation to Arithmetic Geometry”
Jan
31
accepted Homomorphism between finitely generated $k$-algebras of (Krull) dimension 1 preserving maximal properties of ideals.
Jan
31
comment Homomorphism between finitely generated $k$-algebras of (Krull) dimension 1 preserving maximal properties of ideals.
Let me check whether I understand your answer correctly or not. I recall the Zariski lemma states that if $k[x_1,\dots,x_n]/M$ is a field, then $x_i + M$ is algebraic over $k$. If we regard $B = k[x_1,\dots,x_n]/I$, then by the correspondence of ideals, we can regard $B/M \simeq k[x_1,\dots,x_n]/N$ with $M = N/I$. Hence, $B/M$ is a finite dimensional $k$-vector space. Is my realization for the first part correctly?
Jan
31
asked Homomorphism between finitely generated $k$-algebras of (Krull) dimension 1 preserving maximal properties of ideals.
Aug
28
revised Continuity of $\mathfrak{a}$-adic topologies on completion ring and modules
edited title
Aug
28
comment Continuity of $\mathfrak{a}$-adic topologies on completion ring and modules
Thanks for your remind :)
Aug
28
asked Continuity of $\mathfrak{a}$-adic topologies on completion ring and modules
Jul
11
comment A simple way to construct a balanced boolean function by extending a lower dimension one
OH ! Thank you very much! I need to fix my typo!