Timeline for Tensor product of fields
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2017 at 17:13 | comment | added | Neil Strickland | I have edited the answer to correct $k$-module to $A$-module, and to make clear that I am only considering the commutative case. | |
| Aug 31, 2017 at 17:12 | history | edited | Neil Strickland | CC BY-SA 3.0 |
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| Aug 31, 2017 at 17:05 | comment | added | Mare | It has to be $Hom_k(A,k)$ isomorphic to $A$ as $A$-module instead $k$-module I think. Also your equivalences are only true in case $A$ is commutative. My favorite criteria is that it is selfinjective iff its socle is simple in the local case. This might be the quickest thing to check. | |
| Aug 31, 2017 at 17:02 | history | edited | Neil Strickland | CC BY-SA 3.0 |
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| Aug 31, 2017 at 16:53 | comment | added | Mare | Thanks, you gave examples that are not representation-finite. This raises the question if one can give a specific local selfinjective algebra that is not isomorphic to the tensor product of such fields. I added the question. | |
| Aug 31, 2017 at 16:42 | history | answered | Neil Strickland | CC BY-SA 3.0 |