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Results tagged with ra.rings-and-algebras
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user 6503
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.
5
votes
Accepted
Units of the group algebra of a free group
A group $G$ is locally indicable if every nontrivial finitely generated subgroup surjects onto the infinite cyclic group $\mathbb{Z}$.
The following theorem was proven by Higman in 1940 [1]:
Theorem. …
- 2,821
3
votes
Results from abstract algebra which look wrong (but are true)
That there exist finitely presentable non-Hopfian groups. [I still remember my shock when I was first learned this result!]
A group G is Hopfian if every surjective homomorphism $\phi:G\to G$ is in fa …
- 63.1k