/sci/ - Science & Math

>>11792735
Morning & have a nice day + remember to stay hydrated if it's hot there! Planning to have a productive day or a free one?
>please take care of yourself...
Trying to. I reached some sort of katharsis and it feels like I'm regaining some motivation, so maybe I can drop a night or two.

>>11697213
Suppose every (finitely generated) module over your ring has a projective cover. Then your ring is (semi)perfect. What if I told you that if all flat left modules over your ring are projective, your ring has no infinite set of orthogonal idempotents, but it satisfies the descending chain condition on principal right ideals? Suppose that the category of f.g. projective modules over your ring is Krull-Schmidt. Then you can lift all the idempotents from the quotient ring you get by dividing out the Jacobson radical. Seem better?

>>11575962
Oh and, of course, there is Escher with his tesselations and Möbius bands. I remember using the metric of the Poincaré disk to do some tesselations of my own. It's pretty fun, I recommend. All you need is a ruler, a compass and a calculator.

>>11561406
Can't guarantee the first thing will be obtained, but you will become the gf if you keep doing this stuff.