Does there exist a solid concrete detailed textbook on Ring Theory? I'm looking for something like Rotman's book of Group Theory. My background consists of basic Ring Theory/Field Theory from Herstein's Abstract Algebra. I have Rowen's book in my hands right now (library), but it's far too advanced and it skips a lot (that's the purpose of the textbook I know). Anything like Rotman's book would be great because I find Rotman's book to include everything in a detailed fashion without conversing too much, and simply sticking to definitions, theorems, proofs, results and remarks and the occasional motivation at the beginning and end of a chapter. Also, I find the questions to be just right. Some textbooks just have so many problems it's ridiculous. Sure lots of problems is good, but it's not necessary and there exists problem books for this purpose. Rotman uses the right problems and the right number of them, and often refers to them later which is great. Otherwise some books have like 50+ questions at the end of each section and half of the time you don't do the questions the textbook later refers to. It's darn annoying. I think the key to a good textbook is also to have the right/useful problems. Rotman's textbook only has like 6-7 per section on average and I learned more out of that textbook than out of Gallian's and Herstein. Also, Rotman doesn't focus too much on applications either, but he does include interesting ones but also does not make those sections a necessity for later (other textbooks sometimes do by posing lots of questions based on applications). For example, Rotman does included Burnside's Lemma, but not knowing how this Lemma can be applied to certain combinatorial problems will have absolutely no impact on your progress through the book. Yes, I praise Rotman's textbook. I'm currently getting this because it contains material on Artinian rings, simple rings and such. http://www.amazon.com/Introduction-...bs_sr_1?ie=UTF8&s=books&qid=1196400468&sr=1-1 Where can I go from here? My goal is to have a strong algebra background.