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seen Feb 9 '13 at 12:37

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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?