Anonymous at Tue, 29 Oct 2024 02:54:22 UTC No. 16454370

>>16454344
> Ask me anything you know about abstract algebra and we'll see if I'm prepared.

Why are algebraists so much more likely to be schizos or trannies? I've never taken a formal course on algebra, but from self-studying Hungerford and Pinter I didn't see why algebra attracts the band of weirdos it does.

Anonymous at Tue, 29 Oct 2024 02:55:09 UTC No. 16454371

>>16454344
Let A be the quotient of the free algebra C<x,y> by the relations x^2=x+2, y^2=y+2, xyx=yxy.

Prove A is 6-dimensional over C and any irreducible A-module is at most 3 dimensional.

Anonymous at Tue, 29 Oct 2024 02:59:46 UTC No. 16454374

>>16454370
Are analysts any better? honest question.
I used to like analysis until it felt like I hit a dead end. I am starting to appreciate algebra more, I am kinda schizo btw

Anonymous at Tue, 29 Oct 2024 03:00:19 UTC No. 16454375

>>16454370
Autism

Anonymous at Tue, 29 Oct 2024 03:04:16 UTC No. 16454377

>>16454374
Analysts are definitely more anti-social and disagreeable but are much less prone towards transition or schizo nonsense from my experience. Granted, I'm not an analyst. If anything, I'm a probabilist (though more on the information theory side of things than strictly probability theory), but it's analysis heavy enough that it's close enough.

Anonymous at Wed, 30 Oct 2024 12:54:42 UTC No. 16455805

>>16454371
Solve this, OP. You have done your homework right?

Anonymous at Thu, 31 Oct 2024 20:51:39 UTC No. 16457376

>>16454371
I am not op, but let me try:
1,x,y,xy,yx,xyx is a C-basis of A.
An A-module M is irreducible iff M=A/J for some maximal ideal J<A, but these are the maximal ideals of C<x,y> which contain L=(x^2-x-2,y^2-y-2,xyx-yxy), hence any such ideal J must be at least a 3 dimensional vectorspace over C, implying that the dimension of M=A/J cannot be greater than 3.
Is this correct? I am not an algebra person

Anonymous at Thu, 31 Oct 2024 22:51:54 UTC No. 16457519

>>16454377
Probability is a branch of analysis anon

Anonymous at Fri, 1 Nov 2024 14:23:22 UTC No. 16458223

>>16454344
What is difference between additive and multiplicative identity?

Anonymous at Sat, 2 Nov 2024 16:09:36 UTC No. 16459743

>>16454344
What is the payscale for a job in abstract algebra?

Anonymous at Mon, 4 Nov 2024 04:25:30 UTC No. 16461789

>>16458223
0 and 1

Anonymous at Mon, 4 Nov 2024 04:41:56 UTC No. 16461799

>>16454344
describe what a quotient group is (including what the critical property of the subgroup is that makes this the quotient group a group and how this partitions the group into subsets with the same cardinality of the subgroup)

Anonymous at Mon, 4 Nov 2024 17:41:51 UTC No. 16462394

>>16458223
None when viewed as a group. You have to specify your category, bro.