Soham Chowdhury
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 Mar 24 comment Do principal divisors always have degree 0? (from Garrity) @QiaochuYuan Oh, oops. That fixes it. Can you add it as an answer below? Mar 24 asked Do principal divisors always have degree 0? (from Garrity) Mar 19 comment How many combinations of permutation matrices are there? There may be a recurrence relation you can find. Mar 10 accepted A question about classifying conics, from Garrity's book Feb 25 awarded Civic Duty Feb 5 revised Line bundles of the circle "that that" Feb 5 suggested approved edit on Line bundles of the circle Jan 30 accepted Random Wolfram|Alpha identity related to $\sum_{k = 1}^{\infty}{\tan^{-1}}{\frac{1}{k^2}}$ Jan 30 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ @user26857 Good to know, thanks. Jan 30 revised Random Wolfram|Alpha identity related to $\sum_{k = 1}^{\infty}{\tan^{-1}}{\frac{1}{k^2}}$ edited title Jan 29 awarded Notable Question Jan 27 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ @user268578, is this why the localization you give is the "correct one"? Your method uses a set which has $(1,0)$ and $(2^k,1)$ as extra elements (which are not in the "real" multiplicative set). But the latter are all already invertible, so adding a new inverse makes no difference, and an inverse of $(1,0)$ is already going to be present, since if $r$ is the inverse of $(2,0)$, then $2r \times (1,0) = r \times (2,0) = 1$. Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ For anyone stumbling upon these comments: $(0,0)$ is not the multiplicative identity! :P Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ @VJP Why don't you add an answer? The hint was very helpful. Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ Um, I think then every element is zero. Is this justified? $$a = a\times 1 = a\times(r\times (2,0)) = a\times(r\times (0,0)/r) = 0$$Wikipedia seems to do something similar. Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ Quotients of the form $$\frac{(a,b)}{(2, 0)^n}?$$ That probably does not exclude $(1,0)$, since that can be remedied by adding a factor of $2$ to the numerator. Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ i.e. as a quotient of some "well-known" ring, etc. Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ @VJP Yes, I have. I haven't used it much besides proving that localizations at prime ideals are local rings. It seems that this ring is the localization of $\Bbb{R\times R}$ at the multiplicative set $$\{(1,1), (1,0), (2,0), (4,0), \ldots\}$$, but how do I describe that further? Jan 16 comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$ Elementwise addition and multiplication. Jan 16 asked Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$