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visits member for 2 years, 3 months
seen Mar 19 at 16:22

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.


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!
Jul
11
asked A simple way to construct a balanced boolean function by extending a lower dimension one
Jul
9
accepted An exercise in Fulton's Algebraic Curves
Jul
9
comment An exercise in Fulton's Algebraic Curves
Oh! Your proof is totally same with my proof (in my note book)!! Thank you very much!
Jul
9
asked An exercise in Fulton's Algebraic Curves