rschwieb
PhD in Ring and module theory
If you also enjoy ring theory, you might enjoy the Database of Ring Theory.
I also have a blog now. For now I'm just offering advice for people aiming to start a math or math education career path.
If you want, you can buy me a coffee to show support for any of my work online.
Other interests: Clifford algebra/Geometric algebra, Applications of abstract algebra, geometry, Python programming and algorithm design.
Notes for myself:
Prove $R\times S$ is not an integral domain
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
Prove that $A+I$ is invertible if $A$ is nilpotent
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
Order of general- and special linear groups over finite fields.
A linear operator commuting with all such operators is a scalar multiple of the identity.
What are the left and right ideals of matrix ring? How about the two sided ideals?
A ring element with a left inverse but no right inverse?
Explaining the product of two ideals
What's the motivation of the definition of primary ideals?
A ring $R$ which can be written as a direct sum of two ideals.
Ideal contained in a finite union of prime ideals
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