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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 6 months
seen Aug 11 at 15:14

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


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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May
20
answered Factor ring induced by the ideal generated by x(x-1)(x-2)
May
14
revised Errata for Vinberg's “a course in algebra”?
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May
13
comment Summation Indices - How to interpret the zero index?
@penland365 That makes sense - if you've actually proved the telescoping sum formula (which essentially must be by induction), then you'd just be repeating that proof in this case if you did induction here, so telescoping does seem to be the intended strategy.
May
12
comment Summation Indices - How to interpret the zero index?
I don't know the book, so can't check if this makes sense - but this looks like an early exercise in using induction. If you haven't covered induction, then the telescoping sum idea is more likely to be the intended approach. In case this is what's confusing you - there is no sense in which $a_0$ is "always" $0$, so there's nothing to prove there. You seem to be making the observation that $\sum_{i=1}^na_i=\sum_{i=0}^na_i$ if you define $a_0$ to be equal to $0$; this is fine. (But maybe you knew this and I misunderstood you.)
May
12
revised In modular arithmetic is $m^{1/x}$ =! $(m^x)^{-1}$
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May
12
answered In modular arithmetic is $m^{1/x}$ =! $(m^x)^{-1}$
May
6
comment Notation in modulo groups
That sounds promising - $\varphi(m)=|\mathbb{Z}_m^*|$.