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# Questions tagged [ra.rings-and-algebras]

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

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### Finiteness questions for enveloping algebras

Let $\mathfrak{g}$ be a Lie algebra over a field of characteristic $0$. The interesting case for these questions is when $\mathfrak{g}$ is infinite dimensional. Is $U(\mathfrak{g})$ a coherent ...
0answers
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### Newer versions of Mahler's Lemma

I'm trying to find a way to numerically ensure that two constructible numbers are equal (this would be done by a computer). The idea is to find a polynomial $p(x)$ that contains both numbers as roots ...
2answers
182 views

### Complete reducibility and field extension

Let $\pi$ be a representation of a Lie algebra $L$ in a finite-dimensional linear space $V$ over the field $F$. Let $K$ be a field extension of $F$. Let $\pi_K=\pi\otimes K$ be the corresponding ...
1answer
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### Is a specific endomorphism of $A_1$ an automorphism?

Let $k$ be a field of characteristic zero, and let $A_1(k)$ be the first Weyl algebra, namely, the associative non-commutative $k$-algebra generated by $x$ and $y$ subject to the relation $yx-xy=1$. ...
1answer
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### Special idempotents in a commutative ring

Let $R$ be a commutative ring with $1$ and $e$ be an idempotent element of $R$ with the property that if $e=x+y$ (where $x, y\in R$), then there exists $r\in R$ such that either $e=rx$ or $e=ry$. ...

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