I can only suggest 3 , but cannot confirm for you: The one you mentioned, a type of Consolea or Brasiliopuntia brasiliensis. Good luck!

RoRo's second and third guesses are my own too - this looks Brazilian. Since you're in Peoria, Leslie, a strong suggestion is to join the Central Arizona C&S Society - access to books, plants but best of all, maybe, are the people, the books and plants of the Society, all of which will make you a better grower and expand your collection, never mind learning in general about what is and what isn't succulent or cactoid. Aside from the drive for you (to Scottsdale), they're the best way, unless you're a hermit, to improve your growing in quality and quantity, but I think I wrote that already. Opuntias range from northern British Columbia to Tierra del Fuego, so you have a lot to choose from - it's best to have a distinctive feature / flowers to confirm ID, or as you did get it from a knowledgeable grower such as Rosemarie.

Thank you! I looked up the Brasiliensis, it does resemble it quite strongly, but mine doesn't have spines, just the little very fine kind that you need elmer's glue to get out. It looks like there's several different varieties of consolea, I'll have to do some research on that.

It did flower this spring (its only a couple years old) but the flowers weren't very showy. They were kind of a pinkish red, with narrow petals, and I don't think they even opened fully-if they did, they opened and closed before I got a chance to see it.

Thanks for the suggestion about the CACSS, I didn't know about them. I am a bit of a hermit, at least in the summer, but I will definitely check them out. It looks like they have lots of good info on their website, and it would be fun to be able to get together with people who know more about cactus. It's becoming a bit of a passion for me!