Timeline for Tensor product and homomorphism
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2023 at 6:09 | comment | added | marco2013 | @metalspringpro: thanks for the answer. | |
| Feb 10, 2023 at 17:24 | comment | added | metalspringpro | @marco2013 $\operatorname{Tr} N$ denotes the Auslander transpose of $N$. It can be defined by taking a projective presentation $P_1 \xrightarrow{B} P_0 \rightarrow N \rightarrow 0$ and setting $\operatorname{Tr} N:=\operatorname{coker} \operatorname{Hom}_A(B,A)$. It is only unique up to stable equivalence, but this is not an issue for its typical applications. | |
| Feb 10, 2023 at 6:02 | comment | added | marco2013 | @metalspringpro: thanks. What is $\mathrm{Tr} ~N$ ? | |
| Feb 10, 2023 at 5:57 | comment | added | marco2013 | @Martin Brandenburg: thanks for the answer. | |
| Feb 9, 2023 at 7:00 | comment | added | metalspringpro | Just to note. For finitely generated modules over a Noetherian ring, Auslander and Bridger studied this map extensively and used the notion of the Auslander transpose to provide an explicit description of the kernel of this map. It can be described as $\operatorname{Tor}^A_2(\operatorname{Tr} N,M)$. See "Stable Module Theory" by Auslander-Bridger for this and many related results. | |
| Feb 7, 2023 at 22:46 | comment | added | Benjamin Steinberg | Hmm, I guess this one won't make it on the too good to be true list like I hoped :) | |
| Feb 7, 2023 at 22:04 | vote | accept | marco2013 | ||
| Feb 7, 2023 at 21:22 | history | edited | Martin Brandenburg | CC BY-SA 4.0 |
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| Feb 7, 2023 at 21:16 | history | edited | Martin Brandenburg | CC BY-SA 4.0 |
added 464 characters in body
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| Feb 7, 2023 at 21:13 | history | edited | Martin Brandenburg | CC BY-SA 4.0 |
added 464 characters in body
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| Feb 7, 2023 at 21:06 | comment | added | Benjamin Steinberg | If M is flat and N is finitely presented you get an isomorphism | |
| Feb 7, 2023 at 20:53 | history | answered | Martin Brandenburg | CC BY-SA 4.0 |