Questions tagged [noncommutative-algebra]

Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras

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Which CAS can do basic non-commutative differential algebra?

This is a repost of my question at MSE from 7 months ago, to which I haven't been able to find an answer yet. I am looking for a CAS (possibly incl. additional packages/libraries) that can compute ...
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Trace map on Ext group

Let $R$ be a (possibly non-commutative) unital ring and $M$ be a perfect left $R$-module. Then, we have the trace map $$\operatorname{Tr}\colon \mathrm{Hom}_R(M,M)\to R/[R,R]\,.$$ According to the ...
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Multiplicative bases, path algebras, and Ext algebras

I am interested in understanding when a multiplicative basis exists for finite dimensional algebras over an algebraically closed field, and, in particular, Ext-algebras that are finite dimensional. It ...
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Determining the multiplication via addition and some unary operation

It is known that the addition operation in a skew-field $F$ (more generally, in a quasifield) is uniquely determined by the multiplication operation and the unary involutive operation $1_{-}:F\to F$, ...
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Is anything known about the center of the Fomin-Kirillov algebra?

Let $\mathcal{B}_{\mathbb{S}_m}$ be the quotient of the Fomin-Kirillov algebra so that its pairing becomes certainly nondegenerate. This algebra is conjecturally isomorphic to the Fomin-Kirillov ...
• 1,064
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Particular example of a quadratic extension of a nonunital ring

I want to construct a concrete non-unital ring $R$ with the following properties: $R$ is a noncommutative non-unital ring with a right unite $r$ i.e $t.r=t$ for any $t\in R$. $S\subset R$ is a ...
• 163
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Indecomposable injectives over Weyl algebras

Let $A=A_n(\mathbb{C})$ be the $n$-th Weyl algebra over the complex field. Then $A$ is a left Noetherian noncommutative ring. Is there a complete classification of indecomposable injective $A$-modules?...
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