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created: 2022-02-16 14:50:28
modified: 2022-02-16 15:17:52
A brief comparison of what groups and rings do. This shines on some of the similarities between them.
| Groups | Rings |
|---|---|
| Group can act on a set | Rings act on modules (a module is pretty much a vector space) |
| We have LEFT/RIGHT/2-SIDED actions on a set | For modules, we can do the same LEFT/RIGHT/2-SIDED action |
| Cayley's theorem: every group is a symmetry of something | Analogue: every ring is a set of endomorphisms of linear object |