Gregor Bruns
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 Nov20 comment Generators of a finitely generated free module over a commutative ring Note that this would not be a contradiction if $A$ was not commutative. Nov20 comment Free Module $R^{n}$ with zero divisors Why do you think there should be no torsion elements in a free module (over a ring with zero divisors)? The axioms for a free module are clearly satisfied by $R^n$. Nov20 comment How to show that a form on $\mathbb{C}$ defines a holomorphic $1$-form on $\mathbb{C}/\Gamma$? Where are you stuck? How did you define holomorphic 1-forms on $\mathbb{C}/\Gamma$ (a Riemann surface)? This is what you have to check. Do you know what the complex charts are? Nov19 comment $\mathbb{Z}_{11} [x]/\langle x^2-2\rangle$ and $\mathbb{Z}_{11} [x]/\langle x^2-3\rangle$ are not isomorphic You don't have to be sorry, but please don't use the imperative "show" either. How far do you get yourself on this problem? Where are you stuck? Nov19 comment Question of Hartshorne book's Proposion II.(2.6) Could you please elaborate which part exactly you do not understand? In your quote there are a lot of different things happening. Surely you don't want us to explain what a local ring is. Nov19 comment If $A$ is singular, is $A^3+A^2+A$ singular? At least if $p$ does not have a constant term. Nov17 comment Reading circle in mathematics? Thank you for your ideas. It seems like this is the way to go, although it probably will never be as interactive as in other disciplines. I also like the suggestion to do basic number theory, one can never have enough experience with that. Nov17 answered Are all projection maps in a categorical product epic? Nov17 comment Should every line be infinite in both two directions? It depends on what you want. If you consider, e.g., $[0,1]$ as a subspace in its own right, then the line segment $[0,1]$ (in $\mathbb{R}$) is really a line in the subspace $[0,1]$: It goes 'from one end of the space to the other'. So if you want to consider the situation relative to the ambient space, you could add the axiom. If you care about definitions without reference to the embedding, then you should probably not. Nov17 comment Binary notation in Magma Please let me know if you try this and it's actually faster. Nov17 comment Should every line be infinite in both two directions? A line segment/ray does not fit the definition of a line (an induced line) in your link. It does not consist of all points that satisfy the condition. Nov17 answered Binary notation in Magma Nov15 comment Is there no solution to the blue-eyed islander puzzle? In a way, the speech act ensures that everyone has the same information or at least can do the same deductions. Nov15 comment Is there no solution to the blue-eyed islander puzzle? The new information is burrowed in the chain of thought inferences the people do (precisely at the end - the $n=1$ case). The people on the island are quick and logical thinkers, they are not mind-readers. For sure, it does not have to be an outsider who speaks, it could as well be one of the persons on the island. That is why there is this law prohibiting discussing eye-colors. Nov15 comment Is there no solution to the blue-eyed islander puzzle? Why would it not have a solution? You stated the perfectly valid proof (that the 100 blue-eyed people kill themselves after 100 days) yourself. Nov15 comment Help with nilradicals The nilradical contains all the nilpotent elements of a ring $R$, that is the $x\in R$ for which some power $x^n$ will be $0$. Take for example $6\in Z/12$. Is $6^n=0$ for some $n$, modulo $12$? You can just go through the elements of $Z/12$ to get an intuition. Nov15 revised Vakil's Foundations of Algebraic Geometry, Exercise 5.5.E added 3 characters in body Nov15 comment Vakil's Foundations of Algebraic Geometry, Exercise 5.5.E It sure is. However, for the silly sake of tidiness, my solution follows the path the hint suggests (without shortcut). :) Nov15 comment Vakil's Foundations of Algebraic Geometry, Exercise 5.5.E Yup, thank you. I have fixed it. Nov15 revised Vakil's Foundations of Algebraic Geometry, Exercise 5.5.E added 99 characters in body