The Stacks project

Small changes in algebras

Fix grammatical errors and improve readability

Better choice reference in Nakayama's lemma

Thanks to Lucy
https://stacks.math.columbia.edu/tag/07RC#comment-3850

Be more careful about Jacobson radical

Thanks to Brian Conrad
https://stacks.math.columbia.edu/tag/0AMD#comment-3650
https://stacks.math.columbia.edu/tag/0CT7#comment-3651
https://stacks.math.columbia.edu/tag/0BC6#comment-3652
https://stacks.math.columbia.edu/tag/0D48#comment-3653

Improve statement Nakayama's lemma

Thanks to ym
https://stacks.math.columbia.edu/tag/00DV#comment-3431

algebra.tex: Corrections and additional detailing of the proof of Nakayama.

First historical comment

Do not allow \begin{reference} ... \end{reference} on one line for now

Add a reference for Nakayama's lemma

LaTeX

Added a new macro

\def\Im{\text{Im}}

and replaced all occurrences of \text{Im} by \Im

Additional statements in Nakayama's lemma

	Also moved a lemma.

Improve Nakayama's lemma

	Long overdue.

Normalize use of item labels

	Also check for this in parse.py

Whitespace changes

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

More neurotic changes

Clean up labels and references
Add more stringent reference checking to parse.py

	modified:   algebra.tex
	modified:   algebraic.tex
	modified:   categories.tex
	modified:   constructions.tex
	modified:   desirables.tex
	modified:   flat.tex
	modified:   fpqc-descent.tex
	modified:   morphisms.tex
	modified:   schemes.tex
	modified:   scripts/functions.py
	modified:   scripts/make_index.py
	modified:   scripts/parse.py
	modified:   sets.tex
	modified:   sheaves.tex
	modified:   simplicial.tex
	modified:   sites.tex
	modified:   stacks.tex
	modified:   topology.tex

Typos...

	modified:   algebra.tex

	modified:   algebra.tex

	modified:   algebra.tex
	modified:   topology.tex