(no subject)
Hey, how's it going? I'm trying to lower my stress levels. ^_^
The MATH 400 midterm is on Monday, so we don't have any homework to do this week, which is nice cause otherwise I would be doing it right now.
The statement "A ≅ C/B" can be expressed as an exact sequence like this.
ie, G is a subgroup of F (or more precisely, Im G is a subgroup of F) and A ≅ F/ker π = F/G.
Abelian groups all have free resolutions like this:
That's because every abelian group can be written as the quotient of a free abelian group with something (A ≅ F/G with G ⊂ F), and every subgroup of a free group is free (I don't think that I ever learned why that is, but I have just now thought of an argument via transfinite induction, so there).
The slow explanation of Tor continues!
The MATH 400 midterm is on Monday, so we don't have any homework to do this week, which is nice cause otherwise I would be doing it right now.
The statement "A ≅ C/B" can be expressed as an exact sequence like this.
Abelian groups all have free resolutions like this:
That's because every abelian group can be written as the quotient of a free abelian group with something (A ≅ F/G with G ⊂ F), and every subgroup of a free group is free (I don't think that I ever learned why that is, but I have just now thought of an argument via transfinite induction, so there).
The slow explanation of Tor continues!