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842113
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visits member for 2 years, 6 months
seen 8 hours ago

PhD

Interests:

Ring and module theory

Clifford algebra/Geometric algebra

Mathematical physics

Applications of abstract algebra

Misc: Let $m$ and $n$ be integers in the ring of integers. Show that if $m\mathbb Z$ contains $n\mathbb Z$ if and only if $m$ divides $n$


8h
answered Ideals in a polynomial ring over a skew field
18h
comment Is the length of a module over a simple artinian ring an invariant?
@user165614 Yes. If $S$ is a simple module and you take $x\in \oplus_{i\in I} S$, then $x$ is only nonzero on finitely many places, so $x\in \oplus_{i\in F} S$ for a finite subset $F\subseteq I$. If you have finitely many such $x$, they are mutually nonzero only on a finite portion, also. On the rest they are mutually zero.
23h
answered Is the length of a module over a simple artinian ring an invariant?
23h
comment Is the length of a module over a simple artinian ring an invariant?
Not totally sure what you mean by "invariant of a module" here. Can you elaborate?
1d
comment Logical Geometry Challenge
Are you writing "hexagon" when you mean "regular hexagon" or did you intend to allow very exotic hexagons?
1d
comment Strange solution after dividing equation
If we are talking about an equation over a field like $\Bbb R$ or $\Bbb C$, then $x=0$. If two things multiply to zero in a field like $\Bbb R$ or $\Bbb C$, then at least one of them is $0$. And $3$ isn't zero, so...
1d
comment What is an example of a commutative ring with a non-zero element
possible duplicate of True or false? For every element $r$ in a ring $R$, if $r\neq 1$, then $1 − r$ is invertible. This is the third time I've seen this question posted in the past few days. Actually, it looks a lot like you reposted exactly the same question after the previous version was closed for lack of effort. Apologies if I happen to be wrong that you are the same author. But if you are, you ought to learn now that it's unacceptable to repost the same thing.
1d
comment Develop good understanding of Linear Algebra
@shrey You would probably find good books in this question or any of its dozen or so linked questions. Be sure to try searching for your question, especially if you can guess that you are not the first person to ask (like this one.)
2d
comment Irruducible $R$-modules of a ring
It could mean a couple things. Without adding more context, you are rally in a lot better position to find an accurate answer than we are.
2d
comment questions about the taxicab geometry
@MGeometry I started writing a solution at your original question, but haven't completed it. Keep thinking about it in the meantime. You should be able to get the SAS part on your own.
2d
comment questions about the taxicab geometry
@MGeometry : You might find it interesting that these axioms of congruence hold in non-Euclidean geometries too, namely the hyperbolic plane. They are independent of the axiom of parallels which is required in Euclidean geometry. Insisting that you are using "Euclidean axioms" is not quite right, then.
2d
comment questions about the taxicab geometry
You appear to be using Hilbert's axioms of congruence. (Notice the not-all-caps.) Can you confirm this?
2d
comment Verifying certain congruence axioms in taxicab geometry
Are you using Hilbert's axioms of congruence?
2d
comment questions about the taxicab geometry
@MGeometry These are definitely not Euclid's axioms. Btw, "Euclid's 5th postulate" is almost universally synonymous with "the parallel postulate." So now you can see what a mess you can get in with this numbering business.
2d
revised Verifying certain congruence axioms in taxicab geometry
better title
2d
comment questions about the taxicab geometry
@MGeometry I'm also just noticing this is a poorly copied duplicate of most of your earlier question. It is not OK to repost the same question like this. Your first question is better written anyway.
2d
comment questions about the taxicab geometry
possible duplicate of justifying axioms of congruence
2d
comment questions about the taxicab geometry
@MGeometry Yes, but even knowing which axioms you're talking about, how do I know what order they're in? Maybe 4 and 5 are interchanged in some books? It's just not clear... but anyhow verifying that they're true seems like off-task behavior. You're looking for something that breaks 6.
2d
comment questions about the taxicab geometry
@GEdgar Good advice: especially when axioms are enumerated in secret code :)
2d
revised questions about the taxicab geometry
better title, tex