Skip to main content

All Questions

Filter by
Sorted by
Tagged with
5 votes
1 answer
132 views

Integral monoid rings and Ore conditions

Consider a cancellative monoid $S$ satisfying the left Ore condition, so it embeds in a group $G=S^{-1}S$. Consider also the integral monoid rings $\mathbb Z[S]$ and $\mathbb Z[G]$. I have two, ...
Simone Virili's user avatar
2 votes
1 answer
310 views

Flatness of submodules of free modules

Are submodules of free $\mathbb{Z}[G]$-modules flat? if not what conditions on $G$ makes it true? $G$ is an infinite group. If $\mathbb{Z}[G]$ is a Prüfer domain then this is true. Can a group ring $...
user127776's user avatar
  • 5,901
2 votes
0 answers
103 views

Lattices with trivial coinvariants for finite groups

Let $G$ be a finite group. A $\mathbb{Z}G$-lattice is a $\mathbb{Z}G$-module that is (as abelian group) a free abelian group of finite rank. Question: Is there a finite group $G$ and a $\mathbb{Z}...
tj_'s user avatar
  • 2,160
5 votes
0 answers
187 views

Any f.p. faithful simple module over a primitive group ring?

Recall that a ring $R$ is primitive if it has a faithful simple left module. Let $G$ be a countable discrete group and $R=\mathbb{k}G$, where $\mathbb{k}$ denotes some field or $\mathbb{Z}$. There ...
Jiang's user avatar
  • 1,528