/sci/ - Science & Math

>>12578860
>Honestly, sites like nlab make me very scared
The few times I went there for enough time I'd sort of think "Good, reminds me that even autism should have its limits." But maybe I don't know the true power of autism yet.

Because I'm seriously mentally damaged, I often say [math]x[/math] when (really deep) in mind I'm actually meaning [math]y\ne x[/math], which makes me sound extremely dumb. I did a bunch of times here, the possible last three are the restriction vs extension I mentioned, and the following two:
>That's the main purpose of the book
I meant to say "I could also use for homology when I need." (just a reaffirmation of its usefulness for me, this time from my end)
>That would be equivalent to "every module is flat".
I meant to say "A module [math]M[/math] is called [math]\cal{L}[/math] if, and only if, all of its submodules are flat." Let's call [math]{\cal{L} }:= \text{ lolicondom}[/math] (you know, all its subs...). The zero module is a lolicondom, also every lolifier is a lolicondom. Not every module is a lolicondom. I don't think every flat module a lolicondom, but I don't have an example right now.
Oh, I actually did see something like lolifiers, way closer than I thought. It's an exercise defining them by your second definition but in the commutative context (with unity, all rings), though the name given is "absolutely flat". Proves that a ring is one iff its finitely generated ideals are direct summands, iff its finitely generated ideals are idempotents, iff every principal ideal is idempotent. There was at least some truth in the voices in my head!
(I know you didn't mean anything, it's partly a form of venting to feel less shitty about myself)
>Semisimple rings
Cool. One step down closer.
>I haven't slept for about 40 hours, oops
You tried and couldn't? Oh my, take care.
I should be sleeping, but I can't say I tried...
>But at least you got some ideas what to check out, I hope.
Yes! Thanks.

>>12578860
>Honestly, sites like nlab make me very scared
The few times I went there for enough time I'd sort of think "Good, reminds me that even autism should have its limits." But maybe I don't know the true power of autism yet.

Because I'm seriously mentally damaged, I often say [math]x[/math] when (really deep) in mind I'm actually meaning [math]y\ne x[/math], which makes me sound extremely dumb. I did a bunch of times here, the possible last three are the restriction vs extension I mentioned, and the following two:
>That's the main purpose of the book
I meant to say "I could also use for homology when I need." (just a reaffirmation of its usefulness for me, this time from my end)
>That would be equivalent to "every module is flat".
I meant to say "A module [math]M[/math] is called [math]\cal{L}[/math] if, and only if, all of its submodules are flat." Let's call [math]\cal{L} := \text{ lolicondom}[/math] (you know, all his subs...). The zero module is a lolicondom, also every lolifier is a lolicondom. Not every module is a lolicondom. I don't think every flat module a lolicondom, but I don't have an example right now.
Oh, I actually did see something like lolifiers, way closer than I thought. It's an exercise defining them by your second definition but in the commutative context (with unity, all rings), though the name given is "absolutely flat". Proves that a ring is one iff its finitely generated ideals are direct summands, iff its finitely generated ideals are idempotents, iff every principal ideal is idempotent. There was at least some truth in the voices in my head!
(I know you didn't mean anything, it's partly a form of venting to feel less shitty about myself)
>Semisimple rings
Cool. One step down closer.
>I haven't slept for about 40 hours, oops
You tried and couldn't? Oh my, take care.
I should be sleeping, but I can't say I tried...
>But at least you got some ideas what to check out, I hope.
Yes! Thanks.