I'm currently reading Ch. 10 in Dummit & Foote (3rd Edition) and towards the end of the first section, it defines an R-algebra. Dummit & Foote do a decent job of motivating certain definitions/ideas, but this one really seems important and just kinda comes out of nowhere. I was wondering if anyone could possibly give me some motivation or intuition to where this idea of an 'algebra' comes from? Thanks!