Timeline for Linearity of a canonical morphism related to scalar extension and coextension
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2018 at 13:32 | comment | added | Uriya First | [Revised comment. Original deleted.] The map $p$ that you are considering is $\mathrm{Hom}_R(q,N)$, where $q:\mathrm{Hom}_R(S,M)→S\otimes_R M$ is defined by $q(v)=1_S\otimes v(1_S)$. Thus, a sufficient condition for $p$ to be $S$-linear is that $q:\mathrm{Hom}_R(S,M)→S\otimes_RM$ is $S$-linear. | |
| Aug 28, 2018 at 13:27 | comment | added | Uriya First | Dear @Fred. I apologize. I misunderstood and though you wanted $p$ to be an isomorphism in addition to being $S$-module homomorphism. I will delete or replace my comment. | |
| Aug 28, 2018 at 12:11 | comment | added | Fred Rohrer | Dear @Uriya, I do not understand your comment. My question is not about $p$ being an isomorphism (in which category?), but about $p$ being $S$-linear. Your reduction shows that if $q$ is $S$-linear, then so is $p$. Can you clarify? | |
| Aug 28, 2018 at 8:57 | history | asked | Fred Rohrer | CC BY-SA 4.0 |