Not just people, but also mathematical objects, can be oppressed! Pushed into the background, silenced, not taught in courses at the appropriate moment. As a result, the development of mathematics is deformed.

For example: the humble "rig", or "ring without negatives".

(1/n)

Any decent modern algebra course will talk about rings. Few dare mention rigs! As a result, these important mathematical objects are left in the cold:

1. The natural numbers N with the usual + and ×
2. The booleans B = {F,T} with "or" and "and".

Crazy! Shameful!

(2/n)

The roots of oppression go deep. Instead of proving theorems about monoids, a typical course in algebra goes straight to *groups*.

Thus the free group on one generator, Z, reigns supreme - look at it! - while the free monoid on one generator, N, is treated like dirt.

(3/n)

Since *groups* are enthroned while monoids are shunned, every algebra class talks about kernels and normal subgroups - but few discuss equalizers and congruence relations, which are more general, more fundamental, and ultimately simpler.

(4/n)

Then, when they throw multiplication into the mix, our courses talk about rings, which are monoids in (AbGp, ⊗), but not rigs, which are monoids in (CommMon, ⊗).

Indeed, it's strangely hard to find a good intro to the tensor product of commutative monoids!

(5/n)

In algebra class we all learn about modules of rings, and discover to our delight that abelian groups are a special case: namely, Z-modules.

Few of us learn about modules of rigs, or learn that commutative monoids are N-modules.

(6/n)

They teach us about the ring of matrices with entries in a ring... but not the rig of matrices with entries in a rig!

Thus, only an elite few learn that "relations" are matrices with entries in the boolean rig B = {F,T}, with matrix operations having important meanings.

(7/n)

I think the exclusion of the booleans from algebra class helps hide the beautiful connections between algebra and logic.

And the exclusion of both booleans and natural numbers must make computer scientists feel abstract algebra is "not for us".

(8/n)

Someday monoids and rigs will become part of a typical algebra class. Don't get me wrong: I love groups and rings. But the beautiful structure of mathematics is hidden if we neglect the wonderful world without negatives.

(9/n, n = 9)