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Results tagged with ra.rings-and-algebras
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user 35416
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.
7
votes
Accepted
Wedderburn decomposition of special linear groups
$\DeclareMathOperator\M{M}\DeclareMathOperator\Gal{Gal}\DeclareMathOperator\End{End}$As has been mentioned in the comments, the question for algebraically closed fields of characteristic $0$ is equiva …
- 13k
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
5
votes
Structure theorem for finitely generated Z[G] modules
The answer to your question is 'no'. Even if you limit yourself to modules that are free over $\mathbb{Z}$, there is no classification known. Indeed, if your abelian group is not cyclic or its order i …
- 13k