Timeline for Question about terminology for a class of "self-modular" mappings between rings
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2021 at 14:10 | comment | added | Benjamin Steinberg | hom_D also doesn't make clear it is a bimodule map and is a ring homomorphism on D | |
| Jul 13, 2021 at 14:08 | comment | added | Yemon Choi | @BenjaminSteinberg That's a good point, which I think I had observed in a vague way in passing but which I hadn't written down. What is slightly odd/annoying is that the map itself has to define the module structure, so as I said in the question ${\rm Hom}_D$ doesn't feel quite right. And, as I keep trying to explain to undergraduates, you can't really say $\theta \in {\rm Hom}_{\theta,D}$... | |
| Jul 13, 2021 at 13:20 | comment | added | Benjamin Steinberg | I don't know a name for this but notice that your condition can be reformulated as follows : $\theta$ restricts to a ring homomorphism on $D$ and if you give $R$ the obvious $D$-bimodule structure and you give $S$ the one induced by the ring homomorphism $\theta|_D$ then $\theta$ is a $D$-bimodule homomorphism. | |
| Jul 12, 2021 at 20:33 | history | asked | Yemon Choi | CC BY-SA 4.0 |