Getting Ready to Ramble

I see that it's been more than a month since I posted the last Ramble. Part of the problem has been the end-of-semester rush. Another, bigger part is that I've been having trouble trying to work out how to describe these developments in algebra without being either simple but misleading or accurate but confusing. Algebra is, in certain respects, the least concrete of the major branches of mathematics; it's also the branch that I'm best versed in, so I tend to underestimate its difficulties to others.  I have an idea or two for the next post now, though, so the Ramble will resume within the next few days. My apologies for the long layoff.