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I am looking for a some text on ring and module theory which focus mainly on semisimplicity and simple rings along with artinian and noetherian properties. Development of structure of semisimple rings and simple artinian rings with enough examples. One book I have refered is Noncommutative rings by T.Y. Lam but I am looking for one level easier than that. I could not understand the proofs for Wedderburn-Artin theorem and Jacobson density theorem. I would love a text enriched with examples and problems.

Can someone please suggest some texts on Introductory level. I am well familiar with basic ring theory (from Gallian) and basic module theory.

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  • $\begingroup$ Jacobson's Basic Algebra II section 3.13, Bhattacharya, Jain & Nagpaul Basic abstract algebra chapter 19 section 3, Dauns' Modules and rings chapter 7, Isaacs Algebra chapter 14. Rowen's Graduate Algebra: Noncommutative View chapter 14 Knapp... Bland... Birkenmeier... Rotman... Nicholson... I have already been able to locate 10 other sources from googlebooks alone because any noncommutative algebra book worth its salt has a proof. But really, there is nothing too strange about Lam's proof. If you find it hard, it'd be worth your while to post questions about the steps you don't get. $\endgroup$ – rschwieb Sep 24 '15 at 13:20
  • $\begingroup$ In addition to the W-A theorem, they also discuss chain conditions. I don't think there are any books that focus only on the subjects you mention because they are typically chapters included in every algebra book. $\endgroup$ – rschwieb Sep 24 '15 at 13:22
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I guess you should look up this book.

"Rings and Their Modules (De Gruyter Textbook) by Paul Bland".

First six chapters include what you have asked.

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There's a new book called "Introduction to Noncommutative Algebra" by Matej Brešar, in the Universitext collection. I haven't read it in detail, but the beginning of it (the first three chapter) seems quite close to what you're looking for.

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I found the following book interesting during my study:

First Course in Non-commutative rings by T. Y. Lam, along with his problem book Exercises in Classical Ring Theory.

I appreciate the way of his writing, selection of topics, and also selection of problems. I always found useful to work out problems, while learning any subject. And, this author has written problem book also, which is an integral part of theory book.

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