All Questions

I'm curious if there are any papers or results about the following scenario: Let $R$ be a commutative ring (I'm interested in particular in the $R = \mathbb{Z}$ case, but fields are okay too), $G$ a ...

I have already posted this on stackexchange I have a question: If k is an arbitrary field then is it true that if $M$ a finite dimensional $k[x, y]$ is semisimple as a $k[x]$ module and also as a $...

Consider two invertible n-by-n matrices, $n>2$, $X$ and $Y$ over a finite field $k$ (say for simplicity $k=\mathbb Z/ \mathbb Z_2$). Is there any reasonable way to check that there is no proper ...

Suppose $V$ is an infinite dimensional $\mathbb{Q}_p$-representation of Lie algebra $\mathfrak{g}$ over $\mathbb{Q}_p$. If its dual representation $V^{\prime}$ is irreducible then, is it always true ...

My question is slightly motivated by basic results in linear algebra, for example, that if $F$ is a field then a surjective linear map $F^n \rightarrow F^n$ is injective. More generally, any ...