# Tagged Questions

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups.

4 views

### For which category (if any) are Lie algebras the algebras of a monad? [migrated]

I was reading about monads recently, and it came to me that the purpose of the category of algebras of a monad seems to be to switch to a "representation" which is easier for computations. Soon after ...
200 views

### Polynomial ring operations on $\mathbb{Z}$

I have asked this on Math Stack Exchange but without answers: The usual ring operations on $\mathbb{Z}$ can be defined via polynomials in $\mathbb{Z}[a,b]$ (when viewing $a,b$ as variables): ...
85 views

### Left- and right-sided principal ideals of quaternions have same index?

One fact about the Lipschitz integers (quaternions of the form $a + bi + cj + dk$ where $a, b, c, d$ are integers) is that the left-sided ideal generated by any element $Q$ has the same index in the ...
32 views

97 views

### the relation between projective and quasi-projective modules

An $R$-module $M$ is called quasi-projective if $\text{Hom}_R(M,M)\to\text{Hom}_R(M,N)$ is surjective for every surjective homomorphism $M\twoheadrightarrow N$. What are the rings $R$ for which every ...
### Criteria for the surjectivity of the reduction map of the $SL_n$-group scheme
Let $R$ be a commutative ring and let $I\subseteq R$ be an ideal. We have a natural projection map $$\pi:SL_n(R)\rightarrow SL_n(R/I)$$ (In the original question I had put $GL_n$ instead of $SL_n$ ...