Bøger af Matej Bresar

The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications.The book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.

This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition.The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory.Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.

Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality.

A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory.