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 Feb 14 awarded Notable Question Nov 20 awarded Popular Question Oct 24 awarded Popular Question Apr 19 awarded Yearling Feb 11 awarded Popular Question Feb 8 accepted When does the cancellation law hold for the ring of polynomials over a field? Feb 8 asked When does the cancellation law hold for the ring of polynomials over a field? Feb 8 accepted Is there a notation for polynomial division? Feb 8 asked Is there a notation for polynomial division? Feb 7 accepted 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 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..