What Every Algebraist Should Know

I found this song in a folder of notes from a Summer School on Commutative Algebra that I attended in Barcelona in the summer of 1996. I have no idea who originally wrote it, so I’m posting it here as a bit of folklore. The top of the page reads, “To the tune of ‘The Birth of the Blues’”. The modification in the sixth verse is made in my handwriting.

update: Mark Green wrote the song. See below.

The complex of Koszul,
the dimension of Krull,
Homological tools,
Littlewood-Richardson rules,
You know it…
That’s what algebraists should know,
They should know.

It’s not good for your brains
To learn too much about chains,
Cohen-Macaulay domains,
Axioms of Eilenberg and Mac Lane’s,
You know it…

A resolution that’s free,
A Hilbert syzygy,
The arithmetic degrees,
Lemma of Artin-Rees,
You know it…

Give up candies and fats,
Learn the Nullstellensatz,
Complete rings using hats,
Find which modules are flat,
You know it…

Noether’s AF+BG,
Sheaf cohomology,
Characteristic p,
You know it…

It would save on frustration,
It wouldn’t end civilization
If every civilized nation
Banned Noether normalization,
You know it… Yeah Wolmer!

An example that’s new,
The theorem of Bezout,
Resolutions of Lascoux,
Serre’s condition S2,
You know it…

The very best sex
Can’t compete with rlex,
A Taylor series ex,
Or the complex of Cech’s,
You know it…

A closure that’s tight,
An adjoint that’s right,
An ideal and its height,
A resolution that’s not finite,
You know it…

Since the world was first made,
They’ve had depth, dimension and grades,
Groups arising from braids,
Computational aids,
You know it…

There is so much to learn
That out you can burn
If you do not discern
The point of no return,
You know it…

To get out of this fix
Alg and geom you should mix,
Find your own bag of tricks,
Until something sticks,
You know it…

So the next time we meet
I will think it quite neat
TO sit at your feet
While you give the lectures and take the heat,
You know it….


Dave Jorgensen told me that he thought Mark Green had written the song. I wrote to Mark, and he confirmed. One minor mystery solved!