Timeline for Artin Jacobson-semisimple rings are semisimple. Constructively, too?
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| Jan 26, 2015 at 13:06 | comment | added | darij grinberg | I'm not really sure about this all. But I don't think that you can constructively prove that the Jacobson radical is zero for a ring which "floats" somewhere between $\left\{0,1,r,1+r\right\}$ and the whole $R$ (e.g., the ring containing $0,1,r,1+r$ and also containing $r^T$ if some given undecidable statement is true). But Artinianity is also far from obvious for these rings. Let me edit my OP actually. | |
| Jan 26, 2015 at 5:05 | history | edited | Pace Nielsen | CC BY-SA 3.0 |
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| Jan 26, 2015 at 4:17 | history | answered | Pace Nielsen | CC BY-SA 3.0 |