The Stacks project

Add Cauchy-Binet to list of basic notions

Thanks to Herman Rohrbach
https://stacks.math.columbia.edu/tag/07DQ#comment-3577

Fix size matrix in algebra

Thanks to Peter Fleischmann and Fan
https://stacks.math.columbia.edu/tag/00DR#comment-3419
https://stacks.math.columbia.edu/tag/00DR#comment-3424

Revised the material in commits Darij Grinberg

Removed the PBW like lemma in commit
b28cd605026f9194c57022c3b301843e52a66f50
Although we should have lemmas like this in the future, it wasn't
necessary for the proof of lemma-finite-finitely-presented-extension.
Instead we moved this lemma later so we can make use of (very
elementary) theory of finite ring maps, thereby reducing to the one
variable case which should be clear to anyone with an undergraduate
course in modern algebra,

Of course this means we *should* add a discussion of the Grobner
basis algorithm and at that point the lemma will be obvious.

algebra.tex: Add a bit of detail and fix a few bugs.

Flattening by blowing up

Still a bit rough, but the arguments are all there.
A fun lemma is that the problem is etale local on the base.
The rest is exactly as in Raynaud-Gruson (the lemma may
be there too, I'm not sure).

Two typos

Tags: Added new tags

Various notions of standard elements

	This is needed as the approach using just what we now call
	"elementary standard" elements wasn't flexible enough for the
	last part of the proof. Or at least we don't know...