### A Quick Algebra Quiz

#### Posted by John Baez

Here’s a quick algebra quiz. It’s really a test of your reflexes when it comes to algebra and category theory. It should take less than a minute if you have the right mental training. If you don’t, you may be doomed.

So, take a deep breath and give it a try.

- Why is a commutative algebra over a field the same thing as a commutative ring under that field?
- What happens if we leave out the word ‘commutative’ both places here?

## Re: A Quick Algebra Quiz

I guess this means I fail the test, but “ring under a field” is not a term I’m familiar with. Googling doesn’t bring up anything relevant…

The only obvious meaning I could think of was a ring that is a subring of the field in question, for example Z is a subring of Q. But Z is definitely not an algebra over Q, so that can’t be what you mean.