8,234 reputation
1644
bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 7 months
seen 12 hours ago

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


Jun
26
comment Building quotient rings
@o2genum I'm not sure this is a concrete question - you already have described the rings! If you want to describe them in another form, you need to be quite specific about what that form should be. Asking whether the first two are isomorphic to $\mathbb{Z}_n$ is a perfectly good question, but "what ring is $\mathbb{Z}[\sqrt{-2}]/(2)$ isomorphic to?" is too open-ended (unless there's a "standard" ring it's isomorphic to that I don't immediately see).
Jun
19
reviewed Approve suggested edit on If $λ \neq 0$ an eigenvalue of matrix $A$ then find an eigenvalue of $\text{adj}\left(A\right)$
Jun
19
comment Is it true that every eigenvalue has at least one eigenvector?
You could in theory define an eigenvalue to be a root of the characteristic polynomial of $f$. Michael's answer provides half of the proof that these two definitions are equivalent.
Jun
17
comment Is the intersection of dense sets dense?
@freebird The complement of a nowhere dense set is always dense - indeed, one definition of a nowhere dense is that the complement of its closure is dense. But the complement of a dense set is not necessarily nowhere dense, as in the example in your question. So you while you can't prove that the intersection of two arbitrary dense sets is dense (because this is false!) the sets $A'$ and $B'$ in your setup have the stronger property that their complements $A$ and $B$ are nowhere dense. I agree with Ittay that this is probably not the best way to think about the problem though.
Jun
16
answered Is $M=\{\frac{1}{k}|k \in \mathbb{N}\}$ closed?
Jun
9
revised Why is $\left( \begin{smallmatrix} x & y \\ y & t \\ \end{smallmatrix} \right)$ orthogonally similar to this?
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Jun
9
answered Formalize definition of subbase of a topology
Jun
5
comment Solving matrices
I don't think I entirely understand your question - but I will try to say something useful. The question you link to asks you to calculate the determinant of the matrix, which you can do without thinking at all about a linear system that the matrix might represent.
Jun
4
comment Questions for first year students at the University.
Some pedantry - I would argue that $1+2+3+\dotsb+100$ already is written as a sum. Maybe you mean "using $\Sigma$-notation" or something like that?
Jun
4
revised Re-arranging a simple formula
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Jun
3
revised Order of $ g= \big(\begin{smallmatrix} \ 1 & 1 \\ 1 & 0 \end{smallmatrix}\big)\in GL_2(\mathbb F_3)\;. $
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May
29
comment Indecomposable quiver representations
Literally, no, because there are several representations with the same dimension - for example, all the vertex simple representations have dimension $1$. But maybe you mean "dimension vector"?
May
20
comment Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.
@Brandon Yes, $x$ can be equal to $y$. (The definition doesn't say anything to rule this out.) But Mark is right, $3$ is not idempotent in $\mathbb{Z}/12\mathbb{Z}$.
May
20
comment Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.
Do your rings have to be commutative? If not, then $2\times2$ matrices over a field will do.
May
20
revised Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.
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May
20
comment Give an example of a ring in which there exist $x,y,z \in R\setminus\{1,0\}$ such that $x$ is a unit, $y$ is nilpotent, and $z$ is idempotent.
If $n$ is prime, then $R$ is a field and so there are no non-zero nilpotents, and no idempotents other than $0$ or $1$. So if there for an example of this form, $n$ is necessarily not prime.
May
20
comment Finding a basis for intersection of two subspaces
A small notational point that lots of people get wrong - the sets you have written are not subspaces. You probably mean that $w_1$ and $w_2$ are the spans of those sets. Also, you should say "a basis", rather than "the basis".
May
20
revised question related to eigen value of matrix
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May
20
answered An idea involving Cartesian products
May
20
revised Factor ring induced by the ideal generated by x(x-1)(x-2)
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