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15 Mar 2024 |
gm_z | In reply to @gm_z:matrix.org if \mathfrak{m} assassinates some element in N , i'm having trouble constructing a map M\to N that \mathfrak{m} assassinates there's probably some way to view this as a certain splitting | 12:58:03 |
gm_z | like M/\mathfrak{m}M is a vector space over R/\mathfrak{m} , and so we have some R/\mathfrak{m} \hookrightarrow M/\mathfrak{m} \overset{\pi}{\to} R/\mathfrak{m} | 13:01:19 |
gm_z | beyond that idk | 13:01:24 |
gm_z | * like M/\mathfrak{m}M is a vector space over R/\mathfrak{m} , and so we have some R/\mathfrak{m} \hookrightarrow M/\mathfrak{m}M \overset{\pi}{\to} R/\mathfrak{m} | 13:01:35 |
gm_z | oh right then we have M \twoheadrightarrow M/\mathfrak{m}M \overset{\pi}{\to} R/\mathfrak{m} \hookrightarrow N | 13:03:48 |
gm_z | which is assassinated | 13:03:58 |
16 Mar 2024 |
Bowuigi | "Assassinated" is an actual mathematical term? That is pretty odd ngl, I will add it to the list of weird math terms right next to "Anhilates" | 02:51:43 |
polymechanos | In reply to @bowuigi---now-more-based:kde.org "Assassinated" is an actual mathematical term? That is pretty odd ngl, I will add it to the list of weird math terms right next to "Anhilates" never heard of it | 18:38:22 |
18 Mar 2024 |
gm_z | if R is a ring, then a prime ideal \mathfrak{p}\subset R assassinates an element m of an R -module M if rm = 0 \iff r\in\mathfrak{p} | 22:13:25 |
19 Mar 2024 |
Bowuigi | I only understood "prime", "ring" and "element", but apparently when the subset p of the ring R such that ∀r ∈ p. rm = 0 for some m in an R -module M is denoted as "p assasinates m ∈ M " | 02:08:09 |
Bowuigi | Assasination involves anhilation | 02:08:36 |
gm_z | no, assassination is more precise | 06:23:41 |
gm_z | the if and only if also mandates that elements not in \mathfrak{p} will not make rm zero | 06:24:05 |
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Bowuigi | That makes sense | 23:40:05 |
Bowuigi | Do common examples of this exist? | 23:40:28 |
Bowuigi | Because it sounds very specific | 23:40:45 |
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