2,210 reputation
417
bio website
location
age
visits member for 2 years, 7 months
seen Feb 9 '13 at 12:37

Feb
7
comment If $ R $ is a commutative ring with unity, then how do I prove: $ a \neq 0, ~ b \neq 0 \Longrightarrow a \cdot b \neq 0 $?
@Brian Do you mean, for any polynomial ring $R[X]$, $\deg f(X) + \deg g(X)$ may not be equal to $\deg f(X)g(X)$, where they are polynomials? What would be the weakest algebraic structure which makes that possible?
Feb
7
comment If $ R $ is a commutative ring with unity, then how do I prove: $ a \neq 0, ~ b \neq 0 \Longrightarrow a \cdot b \neq 0 $?
•means multiplication here. I dunno how to write small circle in Latex..
Feb
7
asked If $ R $ is a commutative ring with unity, then how do I prove: $ a \neq 0, ~ b \neq 0 \Longrightarrow a \cdot b \neq 0 $?
Feb
5
comment How do I define Polynomial ring $R[x]$ over a commutative ring $R$ with unity?
Thank you. Just for clarity, isn't your argument exactly the same as that i posted?
Feb
5
accepted How do I define Polynomial ring $R[x]$ over a commutative ring $R$ with unity?
Feb
5
comment How do I define Polynomial ring $R[x]$ over a commutative ring $R$ with unity?
Aha! I wonder why author of my textbook didn't write that one simple word 'sequence'.. Thank you
Feb
5
asked How do I define Polynomial ring $R[x]$ over a commutative ring $R$ with unity?
Feb
4
comment How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
@rschwieb Yes, I made that assumption. Thank you!
Feb
4
comment How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
@rschwieb For example, $Z_2=\{0,1\}$ is a field if $1+1=0, 1+0=1, 0•0=0, 1•0=0$. Here, polynomials $f(x)=x^2 + x + 1$ and $g(x)=1$ are not equal polynomials, but they are equal functions.
Feb
4
comment How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
@rschwieb I was confused with the notion "$=$". Is there a special notation to distinguish "Equivalence in $F[X]$" from "equivalence in $F$"? I don't understand why one does not use some equivalence notation such as $\equiv$ for polynomials..
Feb
4
accepted How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
Feb
4
comment How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
@Math This is an exercise in my book, so I'm trying to prove it myself. There is no reference.
Feb
4
asked How do i prove that any two distinct irreducible monic polynomials in a field are relatively prime?
Feb
4
accepted Is there a ring which doesn't satisfy Division Algorithm for polynomials?
Feb
4
asked Is there a ring which doesn't satisfy Division Algorithm for polynomials?
Jan
25
comment Lebesgue measure, Borel sets and Axiom of choice
It's very clear now. Thank you!
Jan
25
accepted Lebesgue measure, Borel sets and Axiom of choice
Jan
25
comment Lebesgue measure, Borel sets and Axiom of choice
Isn't Axiom of countable choice necessary to prove the 'Existence of a completion of Borel measure'? If we cannot prove the existence of the lebesgue measure, how does that make sense to say "There exists a non-Lebesgue measurable set is unprovable in ZF"?
Jan
25
comment Lebesgue measure, Borel sets and Axiom of choice
@Michael I have searched both here and mathoverflow before i post this question, but i couldn't find it. Would you please tell me the link?
Jan
25
revised Lebesgue measure, Borel sets and Axiom of choice
added 1 characters in body