# Questions tagged [group-rings]

A group ring $R[G]$ is a ring constructed in a natural way from a ring $R$ and a group $G$.

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### Optimizing computations with nilpotents in a group algebra

Of course, I have a very concrete problem at hand, which has been vexing me for about a year now. But let me start with a question that has a better chance of having been answered. Let $G$ be a ...
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### Does $M$ satisfy the descending chain conditions on $\mathbb{Z}G$-retracts?

‎Let $H$ be a subgroup of $G$‎. ‎Then a homomorphism $r:G\to H$ is said to be a retraction if the inclusion homomorphism $i:H\hookrightarrow G$ is a right inverse of $r$‎, ‎i.e‎. ‎$r(x)=x$ for all ...
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### Units in group rings in SAGE

Is there a recorded/known SAGE code to compute units in integral group rings for finite abelian groups ? I would be happy with a code that only works for cyclic groups. I sort of know how to ...
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### Topology of the Malcev-Neumann group ring

For a ring $R$ and a group $G$ the group ring $R[G]$ consist of maps from $G$ to $R$ with finite support. It was shown that if the group is fully ordered them this ring can be embedded in a division ... 70 views

### Primitive group rings and endomorphism rings

It is known that, for any group $G$, there exists a group $H$ containing $G$ such that the group ring $F[H]$ for some field $F$ is primitive, see Formanek, Edward; Snider, Robert L., Primitive group ... 63 views

### A question to the Wedderburn-Mal’cev decomposition

Excuse me, I saw the result on the Wedderburn-Mal’cev decomposition of unital compact rings which M.I. Ursul and A. Tripe introduced in the attached file. However, I cannot contact them because ...
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### Center of a monoid ring

According to the Wikipedia page the center of a group ring $R[G]$ is the set: $$\{ p | \forall g,\, h \in G.\, p(g) = p(hgh^{-1}) \}$$ i.e. class functions which do not distinguish elements of the ... 130 views

### Embedding a monoid into a group via its monoid ring

Suppose I have a monoid $(M,\, \cdot,\, e)$ equipped with a monoid homomorphism $\textrm{length} : M \rightarrow \mathbb{N}_+$ into the monoid of natural numbers under addition where $e$ is the only ... 83 views

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