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Results tagged with noncommutative-rings
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user 35416
Questions about rings that are not necessarily commutative.
14
votes
Algebra with a certain abelian group as the multiplicative group
I am going to assume that by "algebra" you simply mean a ring.
The answer is "no", in general. For example $\mathbb{Z}/5\mathbb{Z}$ is not the unit group of a ring. Indeed, suppose it was the unit gro …
- 13k
7
votes
Must a finitely generated projective module over a group ring with vanishing coinvariants be...
This is true when $G$ is finite. This follows from a theorem of Swan [1], which asserts that all projective $\mathbb{Z}[G]$-modules are locally free, i.e isomorphic to a free module over $\mathbb{Z}_p …
- 13k