The Stacks project

Better proof of tricky lemma

Thanks to David Rufino who sent a sort of pull request which I then
applied on the command line and edited.

Try to use L/K notation for field extensions

We could also try to consistenly use "field extension" and not just
"extension" and consistently use "ring extension", etc.

Some more spell checking

Typos and clarification

Thanks to Keenan Kidwell
http://stacks.math.columbia.edu/tag/06RU#comment-734
http://stacks.math.columbia.edu/tag/01WS#comment-735
http://stacks.math.columbia.edu/tag/056N#comment-736
http://stacks.math.columbia.edu/tag/04KM#comment-738
http://stacks.math.columbia.edu/tag/030W#comment-740

More details proof characterization separable field extensions

Thanks to Filip Chindea
http://stacks.math.columbia.edu/tag/030W#comment-387

{\rm d} ---> \text{d}

Whitespace changes

Added new tags

	modified:   tags/tags

Continuing adding material to algebra.tex:

	Power series ring over a Noetherian ring is Noetherian
	Integral closure commutes with localization
	Completions of Noetherian rings are Noetherian
	Taking modules of differentials commutes with colimits
	Better characterization of formally smooth ring maps
	Short exact sequence of modules differentials associated to
		formally smooth ring map
	Formal smoothness lifts along small deformations
	Bunch of lemmas with goal to characterize separable field
		extensions as formally smooth field extensions
	Cohen rings are formally smooth
	Proof of Cohen structure theorem

	modified:   algebra.tex
	modified:   spaces.tex

Continuing adding material to algebra.tex:

	Power series ring over a Noetherian ring is Noetherian
	Integral closure commutes with localization
	Completions of Noetherian rings are Noetherian
	Taking modules of differentials commutes with colimits
	Better characterization of formally smooth ring maps
	Short exact sequence of modules differentials associated to
		formally smooth ring map
	Formal smoothness lifts along small deformations
	Bunch of lemmas with goal to characterize separable field
		extensions as formally smooth field extensions
	Cohen rings are formally smooth
	Proof of Cohen structure theorem

	modified:   algebra.tex
	modified:   spaces.tex

Starting to write more algebra:
	Transcendence degree of field extensions
	Separability of field extensions
	Modified section on base change of algebras over fields
	Formal smoothness for extensions of fields
	Cohen rings
	Cohen structure theorem
	Nagata rings
	Japanese rings
	Ascent of normality

	modified:   algebra.tex