This work deals with basic types of rings, such as simple rings, prime and semiprime rings, etc. Along the way, the results are being adjusted to hold also for algebras, since the main goal of the thesis is to prove Wedderburn’s structure theorem for finite dimensional algebras. The concept of a module is emphasised in the text. It is often used when proving some of the important results, and, moreover it plays a key role in introducing the notion of a primitive ring. The latter is used in the formulation of Jacobson Density Theorem, which provides the necessary tool to prove Wedderburn’s structure theorem.
|
