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Algebra

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Rings and algebras, operator algebras, commutative algebra, quantum algebra, group theory, representation theory || part of #mathematics-on:matrix.org20 Servers

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7 Mar 2024
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15 Mar 2024
@gm_z:matrix.orggm_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:matrix.orggm_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:matrix.orggm_zbeyond that idk13:01:24
@gm_z:matrix.orggm_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:matrix.orggm_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:matrix.orggm_zwhich is assassinated13:03:58
16 Mar 2024
@bowuigi---now-more-based:kde.orgBowuigi"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:matrix.orgpolymechanos
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:matrix.orggm_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---now-more-based:kde.orgBowuigi 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---now-more-based:kde.orgBowuigiAssasination involves anhilation02:08:36
@gm_z:matrix.orggm_zno, assassination is more precise06:23:41
@gm_z:matrix.orggm_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---now-more-based:kde.orgBowuigiThat makes sense23:40:05
@bowuigi---now-more-based:kde.orgBowuigiDo common examples of this exist?23:40:28
@bowuigi---now-more-based:kde.orgBowuigiBecause it sounds very specific23:40:45
20 Mar 2024
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24 Mar 2024
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26 Mar 2024
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29 Mar 2024
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