Book for semisimple rings.

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.