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visits member for 2 years
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PhD

Interests:

Ring and module theory

Clifford algebra/Geometric algebra

Mathematical physics

Applications of abstract algebra


8h
answered prove that if $a$ is not a unit in $\mathbb Z$/m$\mathbb Z$ then $a$ is a zero divisor in $\mathbb Z$/m$\mathbb Z$?
8h
comment If $M$ is Noetherian, then $R/\text{Ann}(M)$ is Noetherian, where $M$ is $R$-module
For commutative rings this is true (Stefano's proof being a good solution), but there exists a noncommutative ring which isn't Noetherian and which has a faithful simple module. That module is of course finitely generated (being cyclic) and its annihilator is zero, so the quotient by the annihilator is clearly not a Noetherian ring or module.
9h
comment Unique non trivial ideal in CFM(k)
Column finite matrix rings over very large index sets can have more ideals than just three. We can only guess in this case the user is thinking of the countable index-set case, where there are only three ideals.
10h
revised 5 digit number $a6a41$ divisible by 9
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11h
answered 5 digit number $a6a41$ divisible by 9
12h
comment Geometry after Khan academy's tutorials
Sounds like a plan, although you'll probably need humans to give feedback on your proofs too. Luckily we do that here. Being comfortable with proofs is a great investment.
19h
comment General linear group/special linear group, isomorphic to R^(*)
I don't follow the 1/det(A) comment. It's easy enough to manufacture a no singular matrix with determinant r. Just put r in the 1,1 position, and 1's on the rest of the diagonal, and zeros elsewhere.
1d
answered Definition of factorial function
1d
comment Geometrical place involving circles.
This is very strange that you accepted the previous question's answer but are asking again here. I notice the wording is slightly different "find the place" and "find the equation," but aren't those the same thing in this situation? The solutions at that answer gave equations (or hinted at how to find the equation) anyhow.
1d
comment Prove that a non-cyclic group of order a² has exactly a+3 subgroups.
@Morpheus What do you think about these sets being distinct subgroups of $C_4\times C_4$?
1d
comment Prove that a non-cyclic group of order a² has exactly a+3 subgroups.
Hi: welcome to math.SE! Questions which are just statements of problems are usually pretty poorly received... you would improve your chances of getting better help faster if you include what you've tried so far! It only takes a minute or two, and it really goes a long way for helping people help you.
1d
answered Prove that a non-cyclic group of order a² has exactly a+3 subgroups.
1d
comment Are roots of unity in hypercomplex algebras well defined?
What definition of "root of unity" are you using that doesn't transfer directly to any ring?
1d
answered Are roots of unity in hypercomplex algebras well defined?
1d
comment Geometry after Khan academy's tutorials
Have you ever taken math courses where exercises were mainly proofs? I don't know if one would want to jump into something at the level of manifolds without being comfortable with proofs first.
1d
answered Geometry after Khan academy's tutorials
1d
answered How to show $\mathbb{Z}[x]/<2,x>$ is isomorphic to $Z_2$
2d
revised Question on geometry based on Ceva's theorem
added wikilinks to help readers
2d
comment Every vector space has a basis using minimal spanning set.
@Prism Shhh! It is recovering from surgery... :)
2d
revised Every vector space has a basis using minimal spanning set.
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