Timeline for $R$ is a UFD iff $R_{\frak{m}}$ is a UFD?
Current License: CC BY-SA 4.0
6 events
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| Jun 18, 2022 at 21:38 | history | edited | David Lampert | CC BY-SA 4.0 |
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| Jun 18, 2022 at 21:32 | comment | added | David Lampert | @PaceNielsen You are right, I sloppily had thought $y_1-1$ was pure grade but this is wrong. I think we can salvage something by changing $\mathbb{Q}$ to $\mathbb{F}_2$ and using $\mathbb{Q}$-grading instead of $\mathbb{N}$-grading but that wouldn't answer the original question. | |
| Jun 18, 2022 at 21:29 | history | edited | David Lampert | CC BY-SA 4.0 |
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| Jun 18, 2022 at 19:24 | comment | added | Pace Nielsen | David, I don't understand how the embedding in $\mathbb{Q}[[x]]$ gives $R$ an $\mathbb{N}$-grading. For example, what are the finitely many graded components of $y_1$? | |
| Jun 18, 2022 at 18:44 | comment | added | It'sMe | My follow-up question is- can we find a counter example where the ring is a quotient of a polynomial ring in finitely many variables, over algebraically closed field? | |
| Jun 18, 2022 at 18:39 | history | answered | David Lampert | CC BY-SA 4.0 |